This is the second volume in a subseries of the Lecture Notes in Mathematics called Lévy Matters, which is published at irregular intervals over the years. Each volume examines a number of key topics in the theory or applications of Lévy processes and pays tribute to the state of the art of this rapidly evolving subject with special emphasis on the non-Brownian world. The expository articles in this second volume cover two important topics in the area of Lévy processes. The first article by Serge Cohen reviews the most important findings on fractional Lévy fields to date in a self-contained piece, offering a theoretical introduction as well as possible applications and simulation techniques. The second article, by Alexey Kuznetsov, Andreas E. Kyprianou, and Victor Rivero, presents an up to date account of the theory and application of scale functions for spectrally negative Lévy processes, including an extensive numerical overview.
This book provides an up-to-date overview of results in rigid body dynamics, including material concerned with the analysis of nonintegrability and chaotic behavior in various related problems. The wealth of topics covered makes it a practical reference for researchers and graduate students in mathematics, physics and mechanics. Contents Rigid Body Equations of Motion and Their Integration The Euler – Poisson Equations and Their Generalizations The Kirchhoff Equations and Related Problems of Rigid Body Dynamics Linear Integrals and Reduction Generalizations of Integrability Cases. Explicit Integration Periodic Solutions, Nonintegrability, and Transition to Chaos Appendix A : Derivation of the Kirchhoff, Poincaré – Zhukovskii, and Four-Dimensional Top Equations Appendix B: The Lie Algebra e(4) and Its Orbits Appendix C: Quaternion Equations and L-A Pair for the Generalized Goryachev – Chaplygin Top Appendix D: The Hess Case and Quantization of the Rotation Number Appendix E: Ferromagnetic Dynamics in a Magnetic Field Appendix F: The Landau – Lifshitz Equation, Discrete Systems, and the Neumann Problem Appendix G: Dynamics of Tops and Material Points on Spheres and Ellipsoids Appendix H: On the Motion of a Heavy Rigid Body in an Ideal Fluid with Circulation Appendix I: The Hamiltonian Dynamics of Self-gravitating Fluid and Gas Ellipsoids
Russia first encountered Alaska in 1741 as part of the most ambitious and expensive expedition of the entire eighteenth century. For centuries since, cartographers have struggled to define and develop the enormous region comprising northeastern Asia, the North Pacific, and Alaska. The forces of nature and the follies of human error conspired to make the area incredibly difficult to map. Exploring and Mapping Alaska focuses on this foundational period in Arctic cartography. Russia spurred a golden era of cartographic exploration, while shrouding their efforts in a veil of secrecy. They drew both on old systems developed by early fur traders and new methodologies created in Europe. With Great Britain, France, and Spain following close behind, their expeditions led to an astounding increase in the world’s knowledge of North America. Through engrossing descriptions of the explorations and expert navigators, aided by informative illustrations, readers can clearly trace the evolution of the maps of the era, watching as a once-mysterious region came into sharper focus. The result of years of cross-continental research, Exploring and Mapping Alaska is a fascinating study of the trials and triumphs of one of the last great eras of historic mapmaking.
Biological Experiments in Space: 30 Years Investigating Life in Space Orbit covers investigations of plant, algae, animals, fish, microorganisms and tissue cultures on space flights, beginning with the first orbital space station on Salyut 1. The book includes results on the influence of the entire complex of physical factors associated with spaceflight on biological systems, including analysis of the impact of microgravity on organisms, as well as the effects of electric and magnetic fields. This book offers important insights for researchers of space biology and astrobiology, as well as space agency and industry specialists developing future space stations and missions. Lack of gravity, temperature and chemical gradients, magnetic and electrical fields, spectral composition and intensity of light, and high-energy cosmic radiation influence many important metabolic and physiological processes in animals, plants, and microorganisms, as well as transfer phenomena in and around them. Success of future space exploration depends on understanding the effects of these factors on biological organisms and developing appropriate countermeasures, aimed at improving growth, development, and reproduction in microgravity. - Includes results on the influence of the entire complex of physical factors associated with spaceflight on a range of biological systems - Analyzes the impacts of microgravity, as well as electric and magnetic fields, on organisms - Covers pioneering investigations of plants, algae, animals, fish, microorganisms and tissue culture in space flights
The book is devoted to the physics of plasma at high density, which has been compressed so strongly that the effects of interparticle interactions and non-ideality govern its behavior. Interest in this non-traditional plasma has been generated in recent years when states of matter with high concentration of energy became accessible experimentally as the basis of modern technologies and facilities. The greatest part of the matter in the Universe is in this exotic state. In this book, the methods of generation and diagnostics of strongly coupled plasmas are presented, along with the main theoretical methods and experimental results on thermodynamical, kinetic and optical properties. Particular attention is given to fast developing modern directions of strongly coupled plasma physics such as metallization of dielectrics and dielectrization of metals, non-neutral plasmas, dusty plasmas and their crystallization. The book is written for physicists and astrophysicists, engineers, and material scientists.
This book offers a systematic and rigorous treatment of continuous-time Markov decision processes, covering both theory and possible applications to queueing systems, epidemiology, finance, and other fields. Unlike most books on the subject, much attention is paid to problems with functional constraints and the realizability of strategies. Three major methods of investigations are presented, based on dynamic programming, linear programming, and reduction to discrete-time problems. Although the main focus is on models with total (discounted or undiscounted) cost criteria, models with average cost criteria and with impulsive controls are also discussed in depth. The book is self-contained. A separate chapter is devoted to Markov pure jump processes and the appendices collect the requisite background on real analysis and applied probability. All the statements in the main text are proved in detail. Researchers and graduate students in applied probability, operational research, statistics and engineering will find this monograph interesting, useful and valuable.
Entropy Randomization in Machine Learning presents a new approach to machine learning—entropy randomization—to obtain optimal solutions under uncertainty (uncertain data and models of the objects under study). Randomized machine-learning procedures involve models with random parameters and maximum entropy estimates of the probability density functions of the model parameters under balance conditions with measured data. Optimality conditions are derived in the form of nonlinear equations with integral components. A new numerical random search method is developed for solving these equations in a probabilistic sense. Along with the theoretical foundations of randomized machine learning, Entropy Randomization in Machine Learning considers several applications to binary classification, modelling the dynamics of the Earth’s population, predicting seasonal electric load fluctuations of power supply systems, and forecasting the thermokarst lakes area in Western Siberia. Features • A systematic presentation of the randomized machine-learning problem: from data processing, through structuring randomized models and algorithmic procedure, to the solution of applications-relevant problems in different fields • Provides new numerical methods for random global optimization and computation of multidimensional integrals • A universal algorithm for randomized machine learning This book will appeal to undergraduates and postgraduates specializing in artificial intelligence and machine learning, researchers and engineers involved in the development of applied machine learning systems, and researchers of forecasting problems in various fields.
This extraordinary book charts the development of Russia’s relations with the Middle East from the 1950s to the present. It covers both high and low points – the closeness to Nasser’s Egypt, followed by reversal; the successful invasion of Afghanistan which later turned into a disaster; the changing relationship with Israel which was at some time surprisingly close; the relationship with Syria, which continues to be of huge significance; and much more. Written by one of Russia’s leading Arabists who was himself involved in the formation and implementation of policy, the book is engagingly written, extremely insightful, telling us things which only the author is in a position to tell us, and remarkably frank, not sparing senior Soviet and Russian figures from criticism. The book includes material based on the author’s conversations with other leading participants.
The present book carefully studies the blow-up phenomenon of solutions to partial differential equations, including many equations of mathematical physics. The included material is based on lectures read by the authors at the Lomonosov Moscow State University, and the book is addressed to a wide range of researchers and graduate students working in nonlinear partial differential equations, nonlinear functional analysis, and mathematical physics. Contents Nonlinear capacity method of S. I. Pokhozhaev Method of self-similar solutions of V. A. Galaktionov Method of test functions in combination with method of nonlinear capacity Energy method of H. A. Levine Energy method of G. Todorova Energy method of S. I. Pokhozhaev Energy method of V. K. Kalantarov and O. A. Ladyzhenskaya Energy method of M. O. Korpusov and A. G. Sveshnikov Nonlinear Schrödinger equation Variational method of L. E. Payne and D. H. Sattinger Breaking of solutions of wave equations Auxiliary and additional results
“It came from nowhere, snapping giant ships in two. No one believed the survivors . . . until now” —New Scientist magazine cover, June 30, 2001 Rogue waves are the focus of this book. They are among the waves naturally - served by people on the sea surface that represent an inseparable feature of the Ocean. Rogue waves appear from nowhere, cause danger, and disappear at once. They may occur on the surface of a relatively calm sea and not reach very high amplitudes, but still be fatal for ships and crew due to their unexpectedness and abnormal features. Seamen are known to be unsurpassed authors of exciting and horrifying stories about the sea and sea waves. This could explain why, despite the increasing number of documented cases, that sailors’ observations of “walls of - ter” have been considered ctitious for a while. These stories are now addressed again due to the amount of doubtless evidence of the existence of the phenomenon, but still without suf cient information to - able interested researchers and engineers to completely understand it. The billows appear suddenly, exceeding the surrounding waves by two times their size and more, and obtaining many names: abnormal, exceptional, extreme, giant, huge, s- den, episodic, freak, monster, rogue, vicious, killer, mad- or rabid-dog waves, cape rollers, holes in the sea, walls of water, three sisters, etc.
This unique book overturns our ideas about non-Euclidean geometry and the fine-structure constant, and attempts to solve long-standing mathematical problems. It describes a general theory of 'recursive' hyperbolic functions based on the 'Mathematics of Harmony,' and the 'golden,' 'silver,' and other 'metallic' proportions. Then, these theories are used to derive an original solution to Hilbert's Fourth Problem for hyperbolic and spherical geometries. On this journey, the book describes the 'golden' qualitative theory of dynamical systems based on 'metallic' proportions. Finally, it presents a solution to a Millennium Problem by developing the Fibonacci special theory of relativity as an original physical-mathematical solution for the fine-structure constant. It is intended for a wide audience who are interested in the history of mathematics, non-Euclidean geometry, Hilbert's mathematical problems, dynamical systems, and Millennium Problems.See Press Release: Application of the mathematics of harmony - Golden non-Euclidean geometry in modern math
Volume I is the first part of the 3-volume book Mathematics of Harmony as a New Interdisciplinary Direction and 'Golden' Paradigm of Modern Science. 'Mathematics of Harmony' rises in its origin to the 'harmonic ideas' of Pythagoras, Plato and Euclid, this 3-volume book aims to promote more deep understanding of ancient conception of the 'Universe Harmony,' the main conception of ancient Greek science, and implementation of this conception to modern science and education.This 3-volume book is a result of the authors' research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the 'Mathematics of Harmony,' a new interdisciplinary direction of modern science. This direction has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the generalized Binet's formulas), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational bases, Fibonacci computers, ternary mirror-symmetrical arithmetic).The books are intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science.
World leading experts give their accounts of the modern mathematical models in the field: Markov Decision Processes, controlled diffusions, piece-wise deterministic processes etc, with a wide range of performance functionals. One of the aims is to give a general view on the state-of-the-art. The authors use Dynamic Programming, Convex Analytic Approach, several numerical methods, index-based approach and so on. Most chapters either contain well developed examples, or are entirely devoted to the application of the mathematical control theory to real life problems from such fields as Insurance, Portfolio Optimization and Information Transmission. The book will enable researchers, academics and research students to get a sense of novel results, concepts, models, methods, and applications of controlled stochastic processes.
The use of mathematical modeling in engineering allows for a significant reduction of material costs associated with design, production, and operation of technical objects, but it is important for an engineer to use the available computational approaches in modeling correctly. Taking into account the level of modern computer technology, this new vo
Volume III is the third part of the 3-volume book Mathematics of Harmony as a New Interdisciplinary Direction and 'Golden' Paradigm of Modern Science. 'Mathematics of Harmony' rises in its origin to the 'harmonic ideas' of Pythagoras, Plato and Euclid, this 3-volume book aims to promote more deep understanding of ancient conception of the 'Universe Harmony,' the main conception of ancient Greek science, and implementation of this conception to modern science and education.This 3-volume book is a result of the authors' research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the 'Mathematics of Harmony,' a new interdisciplinary direction of modern science. This direction has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the generalized Binet's formulas), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational bases, Fibonacci computers, ternary mirror-symmetrical arithmetic).The books are intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science.
The monograph is devoted to the study of initial-boundary-value problems for multi-dimensional Sobolev-type equations over bounded domains. The authors consider both specific initial-boundary-value problems and abstract Cauchy problems for first-order (in the time variable) differential equations with nonlinear operator coefficients with respect to spatial variables. The main aim of the monograph is to obtain sufficient conditions for global (in time) solvability, to obtain sufficient conditions for blow-up of solutions at finite time, and to derive upper and lower estimates for the blow-up time. The abstract results apply to a large variety of problems. Thus, the well-known Benjamin-Bona-Mahony-Burgers equation and Rosenau-Burgers equations with sources and many other physical problems are considered as examples. Moreover, the method proposed for studying blow-up phenomena for nonlinear Sobolev-type equations is applied to equations which play an important role in physics. For instance, several examples describe different electrical breakdown mechanisms in crystal semiconductors, as well as the breakdown in the presence of sources of free charges in a self-consistent electric field. The monograph contains a vast list of references (440 items) and gives an overall view of the contemporary state-of-the-art of the mathematical modeling of various important problems arising in physics. Since the list of references contains many papers which have been published previously only in Russian research journals, it may also serve as a guide to the Russian literature.
“A fresh look at what is perhaps the most famous battle of the Russo-German War from the Soviet perspective.” —The NYMAS Review Much has been written about the Battle of Stalingrad, the Soviet victory that turned the tide of the Second World War. Yet our knowledge and understanding continues to evolve, and this engrossing account by Alexey Isaev brings together previously unpublished Russian archive material—strategic directives and orders, after-action reports, and official records of all kinds—with the vivid recollections of soldiers who were there, on the front lines, reconstructing what happened in extraordinary new detail. The evidence leads him to question common assumptions about the conduct of the battle—about the use of tanks and mechanized forces, for instance, and the combat capability and tenacity of the defeated and surrounded German Sixth Army in the last weeks before it surrendered. His gripping narrative carries the reader through the course of the entire battle from the first small-scale encounters on the approaches to Stalingrad in July 1942, through the intense continuous fighting through the city, to the encirclement, the beating back of the relieving force, and the capitulation of the Sixth Army in February 1943. Military historian Alexey Isaev’s latest book, with maps and illustrations included, is an important contribution to the literature on this decisive battle. It offers a thought-provoking revised view of events for readers already familiar with the story, and a fascinating introduction for those coming to it for the first time.
The book is devoted to some branches of the theory of approximation of abstract differential equations, namely, approximation of attractors in the case of hyperbolic equilibrium points, shadowing, and approximation of time-fractional semilinear problems.In this book, the most famous methods of several urgent branches of the theory of abstract differential equations scattered in numerous journal publications are systematized and collected together, which makes it convenient for the initial study of the subject and also for its use as a reference book. The presentation of the material is closed and accompanied by examples; this makes it easier to understand the material and helps beginners to quickly enter into the circle of ideas discussed.The book can be useful for specialists in partial differential equations, functional analysis, theory of approximation of differential equations, and for all researchers, students, and postgraduates who apply these branches of mathematics in their work.
The structure of sedimentary basins of the Russian Arctic Seas is studied and illustrated by a number of maps, cross-sections and geophysical models. The calculated density models of the Earth crust illustrate the deep structure of the main blocks of the crust. Five major gas-condensate and gas fields are discovered here: three (Shtokman, Ludlov, Ledovoe) in the Barents and two (Leningrad and Rusanov) in the Kara Sea.Geological and geophysical characteristics of the Russian Arctic Sea sedimentary basins allow an estimation of their hydrocarbon potential by comparison with the known world analogues.Total potential resources of giant deposits of hydrocarbons in Russian Arctic Seas are estimated at 470 billion barrels of oil equivalent. The richest resources are the Kara Sea and Laptev Sea. Less rich is Barents Sea. The relatively smaller contribution to the overall estimation of the resources makes the resources of East-Siberian Sea and Chukchi Sea.Development the energy capacity of the continental shelf of Russia can play a stabilizing role in the dynamics of oil and gas production in the period 2010-2020. A key role in developing the capacity of the Arctic shelf oil and gas play is the innovative technology in exploration, production and management of the relevant investment projects. World offshore experience indicates that the combination of these factors is achieved through the formation of international firms and organizations. - Comprehensively assesses the potential oil and gas resources in sedimentary basins within the Russian sector of the Arctic Ocean - Describes the economic and legal challenges to the development of offshore fields in Russia - Explores possible ways and timing to maKe these hydrocarbon resources available to the global market
Stalinism is the name that is used to identify the political and economic systems introduced and implemented by Joseph Stalin in the Soviet Union from the time that Stalin became the supreme power in the Russian Communist Party in 1927 to his death in 1953. During those years, Stalin’s economic policies turned the Soviet Union into an industrial giant with all industries under State management and control. The State was, Stalin and the Party. Stalin’s policies also brought about the collectivization of almost all the agricultural land in the Soviet Union. Each collective farm was regulated by the State. Stalin was a committed Marxian socialist who believed that it was possible to transform the Soviet Union into a Marxian socialist society without assistance from abroad. It was to be a society without the presence of Christianity or any other religious faith. People in the Soviet Union who opposed Stalin’s policies were arrested by Stalin’s feared secret police organizations. The victims were either exiled from the Soviet Union, detained in city prisons, sent to prison labor camps located in Siberia or executed. No Soviet citizen was immune from arrest. This was evident during periods of time when Stalin purged the Russian Communist Party, the only recognized political party in the Soviet Union. The citizens who were declared guilty of the charge or charges brought against them by the State were labeled” enemies of the people.” Family members, close relatives and friends of the victims would suffer serious consequences as well.
Volume II is the second part of the 3-volume book Mathematics of Harmony as a New Interdisciplinary Direction and 'Golden' Paradigm of Modern Science. 'Mathematics of Harmony' rises in its origin to the 'harmonic ideas' of Pythagoras, Plato and Euclid, this 3-volume book aims to promote more deep understanding of ancient conception of the 'Universe Harmony,' the main conception of ancient Greek science, and implementation of this conception to modern science and education.This 3-volume book is a result of the authors' research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the 'Mathematics of Harmony,' a new interdisciplinary direction of modern science. This direction has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the generalized Binet's formulas), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational bases, Fibonacci computers, ternary mirror-symmetrical arithmetic).The books are intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science.
Ion Beam Treatment of Polymers, Second Edition presents the results of polymer investigations and technique development in the field of polymer modification by high-energy ion beams. It shows how to use ion beam equipment in the polymer industry, as well as how to use it to produce new polymer materials. The authors, scientists and researchers active in the field, provide analysis and data from their work, and give an overview of related work by others. The authors focus on wetting, adhesion, hardness, chemical activity, environmental stability, biocompatibility, new synthesis methods, and space flight construction. The technologies of material modification by a beam of high energy ions have wide applications in different fields, from microelectronics to medicine. Historically, ion beam treatment of polymers had fewer applications due to high costs of ion beam equipment and low costs of polymer materials. The modern development of new pulse sources with a high current density and wide ion beams increase the effectiveness of ion beam technology for polymers. - Collates data from many scientists working in polymer chemistry, physics of ion beam implantation, and in development and production of ion beam equipment - Covers industrial and scientific applications of ion beam implanted polymers - Integrates physical and chemical aspects of the processes in polymers treated by ion beams
Chemometrics is the chemical discipline that uses mathematical, statistical and other methods employing formal logic: to design or select optimal measurement procedures and experiments, and -- to provide maximum relevant chemical information by analysing chemical data. Being conceived as a branch of analytical chemistry, chemometrics now is a general approach. It extracts relevant information out of measured data, regardless of their origin: chemical, physical, biological, etc. Chemometrics has been applied in different areas, and most successfully in multivariate calibration, pattern recognition, classification and discriminant analysis, multivariate modelling, and monitoring of processes. The main chemometric principle is a concept of hidden data structures that can be found using methods of multivariate data analysis. These are the well-known statistic tools such as partial least squares (PLS), soft independent modelling of class analogy (SIMCA), principal-component regression (PCR), wavelet analysis, and many others. Current activities of chemometricians fall into two main categories: (1) development of new methods for manipulating multivariate data and (2) new applications of the known chemometric techniques in different areas such as environment control, food industry, agriculture, medicine, and engineering.
This book embraces the entire range of problems associated with phase equilibria in “tungsten – carbon” binary system and related ternary systems, nonstoichiometry, disorder and order in different tungsten carbides, electronic and crystal structure of these carbides. The main application of tungsten carbides is constituent in hardmetals for cutting tools. In the last 20 years, the most active efforts were made in synthesis and application of nanocrystalline tungsten carbide for the production of nanostructured hardmetals. The present book describes in detail different methods for production of nanocrystalline tungsten carbide. The peculiarities of sintering of Co hardmetals from nanocrystalline powders having different particle sizes are discussed. Materials scientists using tungsten carbide to create novel superhard and tough materials will find this book particularly useful.
This book is dedicated to the theory of supernovae, focusing on new computational methods and simulations. It contains three parts: basic principles, numerical methods, and applications. The first part contains a non-formal introduction into the basics of supernovae, Boltzmann kinetic equations — with details of two particles reaction rate calculations — and the transformation of Boltzmann kinetic equations into hydrodynamic elements of statistical physics. It also contains the equation of state for matter of high energy density, with details of calculations for thermodynamic parameters, weak interactions, reaction rate details, and thermonuclear burning. The second part introduces elements of computational physics.The book closes with a presentation of original thought regarding the regime of burning in degenerate carbon-oxygen cores, a neutrino transport in Type II supernovae, a simulation of general relativity (GR) coalescence of neutron stars, aspherical nucleosynthesis in a core-collapse supernova, and thermalization in a pair of plasma winds from a compact strange star.This book brings together generally accepted simulations methods as well as original material written by two respected members of Russian research groups: the Keldysh Institute of Applied Mathematics and Institute of Theoretical and Experimental Physics. It contains the necessary information for a person to start independent research in this fast-developing field, and is therefore an important read for new researchers in this subject.
Stephen Hawking says that the 21st century will be the century of complexity and indeed now systems biology or medicine means dealing with complexity. Both the genome and physiome have emerged in studying complex physiological systems. Computational and mathematical modeling has been regarded as an efficient tool to boost the understanding about living systems in normal or pathophysiological states. Covering applied methodology, basic case studies and complex applications, this volume provides researchers with an overview of modeling and computational studies of physiology (i.e. quantitative physiology), which is becoming an increasingly important branch of systems biology. This book aims to build multi-scale models to investigate functions in living systems and explain how biomolecules, cells, organs, organ systems and organisms carry out the chemical or physical functions. Some of the models addressed are related to gene expression, calcium signalling, neural activity, blood dynamics and bone mechanics. Combining theory and practice, with extensive use of MATLAB, this book is designed to establish a paradigm for quantitative physiology by integrating biology, mathematics, physics and informatics etc. To benefit from this book, the readers are expected to have a background in general physiology and mathematics
This is the second volume in a subseries of the Lecture Notes in Mathematics called Lévy Matters, which is published at irregular intervals over the years. Each volume examines a number of key topics in the theory or applications of Lévy processes and pays tribute to the state of the art of this rapidly evolving subject with special emphasis on the non-Brownian world. The expository articles in this second volume cover two important topics in the area of Lévy processes. The first article by Serge Cohen reviews the most important findings on fractional Lévy fields to date in a self-contained piece, offering a theoretical introduction as well as possible applications and simulation techniques. The second article, by Alexey Kuznetsov, Andreas E. Kyprianou, and Victor Rivero, presents an up to date account of the theory and application of scale functions for spectrally negative Lévy processes, including an extensive numerical overview.
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