A comprehensive overview of weak convergence of stochastic processes and its application to the study of financial markets. Split into three parts, the first recalls the mathematics of stochastic processes and stochastic calculus with special emphasis on contiguity properties and weak convergence of stochastic integrals. The second part is devoted to the analysis of financial theory from the convergence point of view. The main problems, which include portfolio optimization, option pricing and hedging are examined, especially when considering discrete-time approximations of continuous-time dynamics. The third part deals with lattice- and tree-based computational procedures for option pricing both on stocks and stochastic bonds. More general discrete approximations are also introduced and detailed. Includes detailed examples.
This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested in such developments. Beginning graduate or advanced undergraduate students will benefit from this detailed approach to an essential area of probability theory. The emphasis is on concise and efficient presentation, without any concession to mathematical rigor. The material has been taught by the author for several years in graduate courses at two of the most prestigious French universities. The fact that proofs are given with full details makes the book particularly suitable for self-study. The numerous exercises help the reader to get acquainted with the tools of stochastic calculus.
Fragmentation and coagulation are two natural phenomena that can be observed in many sciences and at a great variety of scales - from, for example, DNA fragmentation to formation of planets by accretion. This book, by the author of the acclaimed Lévy Processes, is the first comprehensive theoretical account of mathematical models for situations where either phenomenon occurs randomly and repeatedly as time passes. This self-contained treatment develops the models in a way that makes recent developments in the field accessible. Each chapter ends with a comments section in which important aspects not discussed in the main part of the text (often because the discussion would have been too technical and/or lengthy) are addressed and precise references are given. Written for readers with a solid background in probability, its careful exposition allows graduate students, as well as working mathematicians, to approach the material with confidence.
Organ transplantation has been successfully performed over the last 35 years and the number of organ allograft recipients is steadily increasing. Long-term immunosuppression, necessary for good graft function, inevitably induces undesired effects (particularly infectious and neoplastic ones) among which cutaneous ones are very frequent and potentially life-threatening. This book deals with all aspects of cutaneous disorders that may be encountered in the setting of organ transplantation. It reflects the pioneering work performed since long by Dermatologists in Lyon, in collaboration with teams specialised in kidney, heart, lung, liver and pancreas transplantation.
This book is about discrete-time, time-homogeneous, Markov chains (Mes) and their ergodic behavior. To this end, most of the material is in fact about stable Mes, by which we mean Mes that admit an invariant probability measure. To state this more precisely and give an overview of the questions we shall be dealing with, we will first introduce some notation and terminology. Let (X,B) be a measurable space, and consider a X-valued Markov chain ~. = {~k' k = 0, 1, ... } with transition probability function (t.pJ.) P(x, B), i.e., P(x, B) := Prob (~k+1 E B I ~k = x) for each x E X, B E B, and k = 0,1, .... The Me ~. is said to be stable if there exists a probability measure (p.m.) /.l on B such that (*) VB EB. /.l(B) = Ix /.l(dx) P(x, B) If (*) holds then /.l is called an invariant p.m. for the Me ~. (or the t.p.f. P).
Devoted to a systematic exposition of some recent developments in the theory of discrete-time Markov control processes, the text is mainly confined to MCPs with Borel state and control spaces. Although the book follows on from the author's earlier work, an important feature of this volume is that it is self-contained and can thus be read independently of the first. The control model studied is sufficiently general to include virtually all the usual discrete-time stochastic control models that appear in applications to engineering, economics, mathematical population processes, operations research, and management science.
Dermatology, edited by world authorities Jean L. Bolognia, MD, Joseph L. Jorizzo, MD, and Julie V. Schaffer, MD, is an all-encompassing medical reference book that puts the latest practices in dermatologic diagnosis and treatment at your fingertips. It delivers more comprehensive coverage of basic science, clinical practice, pediatric dermatology, and dermatologic surgery than you’ll find in any other source. Whether you’re a resident or an experienced practitioner, you’ll have the in-depth, expert, up-to-the-minute answers you need to overcome any challenge you face in practice. Find answers fast with a highly user-friendly, "easy-in-easy-out" format and a wealth of tables and algorithms for instant visual comprehension. Get full exposure to core knowledge with coverage of dermatology’s entire spectrum of subspecialties. See just the essential information with "need-to-know" basic science information and key references. Expedite decision making and clarify complex concepts with logical tables, digestible artwork, and easy-to-grasp schematics. Visualize more of the conditions you see in practice with over 3500 illustrations, of which over 1,400 are new: 1,039 clinical images, 398 pathology slides, and 152 schematics. Stay at the forefront of your field with updated treatment methods throughout, as well as an increased focus on patients with skin of color. Get an enhanced understanding of the foundations of dermatology in pathology, the clinical setting, and dermoscopy with a completely rewritten introductory chapter. Better comprehend the clinical-pathological relationship of skin disease with increased histologic coverage. Bolognia’s Dermatology is the ultimate multimedia reference for residents in training AND the experienced practitioner.
Discourse is not just a means of expressing thought; it is also an autonomous body, an act through which we aim to achieve a certain effect. Modern linguistics proposes a broader definition of discourse, as a discrete and unique enunciative process, where the speaker or author makes language concrete through speech (in the Saussurian sense), and describes the various acts (oral, illocutionary, perlocutionary) that discourse performs. This book examines discourse, an object of analysis and criticism, from a wide range of perspectives. Among the concepts explored are the contributions of rhetoric in the art of discourse, the evolution of multiple approaches and the main methods of discourse analysis conducted by a variety of researchers. The book deepens our knowledge and understanding of discourse, a concept on which any research related to information and communication can be based.
A comprehensive introduction to the statistical and econometric methods for analyzing high-frequency financial data High-frequency trading is an algorithm-based computerized trading practice that allows firms to trade stocks in milliseconds. Over the last fifteen years, the use of statistical and econometric methods for analyzing high-frequency financial data has grown exponentially. This growth has been driven by the increasing availability of such data, the technological advancements that make high-frequency trading strategies possible, and the need of practitioners to analyze these data. This comprehensive book introduces readers to these emerging methods and tools of analysis. Yacine Aït-Sahalia and Jean Jacod cover the mathematical foundations of stochastic processes, describe the primary characteristics of high-frequency financial data, and present the asymptotic concepts that their analysis relies on. Aït-Sahalia and Jacod also deal with estimation of the volatility portion of the model, including methods that are robust to market microstructure noise, and address estimation and testing questions involving the jump part of the model. As they demonstrate, the practical importance and relevance of jumps in financial data are universally recognized, but only recently have econometric methods become available to rigorously analyze jump processes. Aït-Sahalia and Jacod approach high-frequency econometrics with a distinct focus on the financial side of matters while maintaining technical rigor, which makes this book invaluable to researchers and practitioners alike.
In answer to the intense development of new financial products and the increasing complexity of portfolio management theory, Portfolio Optimization and Performance Analysis offers a solid grounding in modern portfolio theory. The book presents both standard and novel results on the axiomatics of the individual choice in an uncertain framework, cont
This book introduces several remarkable new probabilistic objects that combine spatial motion with a continuous branching phenomenon and are closely related to certain semilinear partial differential equations (PDE). The Brownian snake approach is used to give a powerful representation of superprocesses and also to investigate connections between superprocesses and PDEs. These are notable because almost every important probabilistic question corresponds to a significant analytic problem.
Offering multidisciplinary guidance to all health care practitioners who provide clinical care for children and adolescents, the 7th Edition of Emans, Laufer, Goldstein’s Pediatric & Adolescent Gynecology has been extensively revised to keep you up to date in this complex field. You’ll find comprehensive coverage of the full spectrum of medical and surgical approaches to common and uncommon problems – everything from infants with vulvar rashes, to the child with early or late onset of puberty, to adolescents and young adults with ovarian cysts or STDs. More than 40 experts in the field, led by editors from Boston Children’s Hospital and Harvard Medical School, have contributed to ensure this classic text remains relevant and useful in daily practice.
This volume by two international leaders in the field proposes a systematic exposition of convergence in law for stochastic processes from the point of view of semimartingale theory. It emphasizes results that are useful for mathematical theory and mathematical statistics. Coverage develops in detail useful parts of the general theory of stochastic processes, such as martingale problems and absolute continuity or contiguity results.
This book presents the first part of a planned two-volume series devoted to a systematic exposition of some recent developments in the theory of discrete-time Markov control processes (MCPs). Interest is mainly confined to MCPs with Borel state and control (or action) spaces, and possibly unbounded costs and noncompact control constraint sets. MCPs are a class of stochastic control problems, also known as Markov decision processes, controlled Markov processes, or stochastic dynamic pro grams; sometimes, particularly when the state space is a countable set, they are also called Markov decision (or controlled Markov) chains. Regardless of the name used, MCPs appear in many fields, for example, engineering, economics, operations research, statistics, renewable and nonrenewable re source management, (control of) epidemics, etc. However, most of the lit erature (say, at least 90%) is concentrated on MCPs for which (a) the state space is a countable set, and/or (b) the costs-per-stage are bounded, and/or (c) the control constraint sets are compact. But curiously enough, the most widely used control model in engineering and economics--namely the LQ (Linear system/Quadratic cost) model-satisfies none of these conditions. Moreover, when dealing with "partially observable" systems) a standard approach is to transform them into equivalent "completely observable" sys tems in a larger state space (in fact, a space of probability measures), which is uncountable even if the original state process is finite-valued.
Edited by world authorities Drs. Jean L. Bolognia, Julie V. Schaffer, Karynne O. Duncan, and Christine J. Ko, Dermatology Essentials, 2nd Edition, provides the fast answers you need on every important aspect of dermatology and guidance on their application in your day-to-day practice. Derived from the renowned authoritative reference work Dermatology, 4th Edition, this on-the-go reference distills the essential information needed to quickly diagnose and manage a wide range of dermatologic disorders—without the need for any additional resources. It's an ideal reference for family medicine and internal medicine physicians, nurse practitioners, physician assistants, and other health care professionals who diagnose, treat, and refer patients with dermatological conditions. - Features a highly user-friendly, "easy-in-easy-out" format and a wealth of tables and schematics for instant visual comprehension. - Helps you visualize more of the conditions you see in practice with over 1,800 typical clinical images, illustrations, and line drawings. - Includes numerous practical tables, intuitive artworks, and logical algorithms to help you avoid diagnostic pitfalls. - Expedites decision making with easily recognizable DDx and Rx sections that provide rapid, direct reference to current guidance and treatment recommendations. Downloadable worksheets are also available. - Features unique introductory chapters that cover the basic principles of dermatology, bedside diagnostics, and clinical approach to a fever and rash—extremely helpful information for the beginner.
Here is a helpful guide, A-to-Z guide on the structures of chemicals implicated in contact dermatitis. It describes each molecule along with its principal name for classification. The dictionary also lists the most important synonyms, the Chemical Abstract Service (CAS) Registry Number that characterizes the substance and its chemical structure, and relevant literature references. This guide is a must-have for each physician involved with the diagnosis and treatment of patients with contact dermatitis and allergic skin disease.
A timely and comprehensive treatment of random field theory with applications across diverse areas of study Level Sets and Extrema of Random Processes and Fields discusses how to understand the properties of the level sets of paths as well as how to compute the probability distribution of its extremal values, which are two general classes of problems that arise in the study of random processes and fields and in related applications. This book provides a unified and accessible approach to these two topics and their relationship to classical theory and Gaussian processes and fields, and the most modern research findings are also discussed. The authors begin with an introduction to the basic concepts of stochastic processes, including a modern review of Gaussian fields and their classical inequalities. Subsequent chapters are devoted to Rice formulas, regularity properties, and recent results on the tails of the distribution of the maximum. Finally, applications of random fields to various areas of mathematics are provided, specifically to systems of random equations and condition numbers of random matrices. Throughout the book, applications are illustrated from various areas of study such as statistics, genomics, and oceanography while other results are relevant to econometrics, engineering, and mathematical physics. The presented material is reinforced by end-of-chapter exercises that range in varying degrees of difficulty. Most fundamental topics are addressed in the book, and an extensive, up-to-date bibliography directs readers to existing literature for further study. Level Sets and Extrema of Random Processes and Fields is an excellent book for courses on probability theory, spatial statistics, Gaussian fields, and probabilistic methods in real computation at the upper-undergraduate and graduate levels. It is also a valuable reference for professionals in mathematics and applied fields such as statistics, engineering, econometrics, mathematical physics, and biology.
This book constitutes the thoroughly refereed post-workshop proceedings of the Third International Workshop on Implementing Automata, WIA'98, held in Rouen, France, in September 1998. The 21 revised full papers presented were carefully selected from the workshop contributions after several rounds of reviewing. The papers are devoted to issues of implementing automata of various types important for areas such as parsing, computational linguistics, speech recognition, text searching, device controlers, distributed systems, and protocol analysis.
This book uses the hypoelliptic Laplacian to evaluate semisimple orbital integrals in a formalism that unifies index theory and the trace formula. The hypoelliptic Laplacian is a family of operators that is supposed to interpolate between the ordinary Laplacian and the geodesic flow. It is essentially the weighted sum of a harmonic oscillator along the fiber of the tangent bundle, and of the generator of the geodesic flow. In this book, semisimple orbital integrals associated with the heat kernel of the Casimir operator are shown to be invariant under a suitable hypoelliptic deformation, which is constructed using the Dirac operator of Kostant. Their explicit evaluation is obtained by localization on geodesics in the symmetric space, in a formula closely related to the Atiyah-Bott fixed point formulas. Orbital integrals associated with the wave kernel are also computed. Estimates on the hypoelliptic heat kernel play a key role in the proofs, and are obtained by combining analytic, geometric, and probabilistic techniques. Analytic techniques emphasize the wavelike aspects of the hypoelliptic heat kernel, while geometrical considerations are needed to obtain proper control of the hypoelliptic heat kernel, especially in the localization process near the geodesics. Probabilistic techniques are especially relevant, because underlying the hypoelliptic deformation is a deformation of dynamical systems on the symmetric space, which interpolates between Brownian motion and the geodesic flow. The Malliavin calculus is used at critical stages of the proof.
The Paris-Princeton Lectures in Financial Mathematics, of which this is the fourth volume, publish cutting-edge research in self-contained, expository articles from outstanding specialists - established or on the rise! The aim is to produce a series of articles that can serve as an introductory reference source for research in the field. The articles are the result of frequent exchanges between the finance and financial mathematics groups in Paris and Princeton. The present volume sets standards with five articles by: 1. Areski Cousin, Monique Jeanblanc and Jean-Paul Laurent, 2. Stéphane Crépey, 3. Olivier Guéant, Jean-Michel Lasry and Pierre-Louis Lions, 4. David Hobson and 5. Peter Tankov.
This is the third volume in the Paris-Princeton Lectures in Financial Mathematics, which publishes, on an annual basis, cutting-edge research in self-contained, expository articles from outstanding specialists, both established and upcoming. Coverage includes articles by René Carmona, Ivar Ekeland/Erik Taflin, Arturo Kohatsu-Higa, Pierre-Louis Lions/Jean-Michel Lasry, and Huyên Pham.
The field of cytokine research is expanding at a rapid pace Contributions from the major leading groups in the world on the structure and biological properties of cytokine and cytokine receptors, as well as integrated reviews on cytokines in various physiological and pathological conditions were presented in three issues of International Reviews of Immunology This collection of articles provided a unique source of information However, important discoveries are emerging very rapidly and some of the reviews written in 1997 are already outdated In this book, the editors assemble reviews that have been updated by their authors to include all the recent publications and unpublished data from the authors' laboratories This volume should serve as an excellent reference source for all those concerned by the multiple faces of cytokines in basic research and in the clinic
From the reviews: "The account is quite detailed and is written in a manner that will appeal to analysts and numerical practitioners alike...they contain everything from rigorous proofs to tables of numerical calculations.... one of the strong features of these books...that they are designed not for the expert, but for those who whish to learn the subject matter starting from little or no background...there are numerous examples, and counter-examples, to back up the theory...To my knowledge, no other authors have given such a clear geometric account of convex analysis." "This innovative text is well written, copiously illustrated, and accessible to a wide audience
Convex Analysis may be considered as a refinement of standard calculus, with equalities and approximations replaced by inequalities. As such, it can easily be integrated into a graduate study curriculum. Minimization algorithms, more specifically those adapted to non-differentiable functions, provide an immediate application of convex analysis to various fields related to optimization and operations research. These two topics making up the title of the book, reflect the two origins of the authors, who belong respectively to the academic world and to that of applications. Part I can be used as an introductory textbook (as a basis for courses, or for self-study); Part II continues this at a higher technical level and is addressed more to specialists, collecting results that so far have not appeared in books.
The focus of this book is the large-scale statistical behavior of solutions of divergence-form elliptic equations with random coefficients, which is closely related to the long-time asymptotics of reversible diffusions in random media and other basic models of statistical physics. Of particular interest is the quantification of the rate at which solutions converge to those of the limiting, homogenized equation in the regime of large scale separation, and the description of their fluctuations around this limit. This self-contained presentation gives a complete account of the essential ideas and fundamental results of this new theory of quantitative stochastic homogenization, including the latest research on the topic, and is supplemented with many new results. The book serves as an introduction to the subject for advanced graduate students and researchers working in partial differential equations, statistical physics, probability and related fields, as well as a comprehensive reference for experts in homogenization. Being the first text concerned primarily with stochastic (as opposed to periodic) homogenization and which focuses on quantitative results, its perspective and approach are entirely different from other books in the literature.
Practical, comprehensive, and updated throughout, the 4th edition of Dermatological Signs of Internal Diseases helps you identify a full range of common and rare systemic diseases early...so they can be managed as effectively as possible. Coverage of new disorders, including nephrogenic fibrosing dermopathy, new treatment options, expanded histopathology content, new color images, online image library and much more...to help you attain definitive diagnoses of internal diseases that manifest on the skin. Best of all, each chapter features an evidence-based approach to diagnosis and treatment so you know you can depend on the clinical recommendations presented. Expert Consult functionality allows you to access the entire contents of the book online at expertconsult.com from any Internet connection. Presents an evidence-based approach so you can depend on the clinical recommendations presented. Covers advice on patient evaluation and lab tests, as well as tables of differential diagnoses, to facilitate diagnosis for every condition. Uses a consistent, user-friendly format for easy reference. Discusses new diseases such as nephrogenic fibrosing dermopathy and new therapies, including biologics, to keep you on the cusp of this rapidly expanding field. Provides improved and expanded histopathology content for a better understanding in this difficult area of diagnosis. Features over 500 full-color illustrations—100 new to this edition—that provide the best possible representations of diseases as they appear in real life. Features a companion website at expertconsult.com with fully searchable text and an image library to enhanced visual guidance.
Nuclear medicine and lung diseases is intended for chest physicians who use nuclear medicine techniques in clinical practice and for nuclear physicians who perform tests in patients with chest disorders. The book is valuable for clinical practice and describes the interrelationship between the two specialities. Chest physicians will be better able to understand the significance of the results of nuclear medicine and nuclear physicians will appreciate more fully the clinical contexts in which nuclear techniques are of value. In the first part the physical and technical principles of nuclear medicine and the physiopathological bases are developed. In the second part the applications of nuclear medicine are presented in separate chapters on chest diseases - diffuse, infiltrative lung diseases, lung tumors, infections, pulmonary embolism, lung function and surgery, AIDS, lung transplantation, chronic obstructive bronchopulmonary diseases and therapy. Nuclear medicine and lung diseases represents the work of 15 French authors led by three main authors.
The 7th International Conference on Implementation and Application of Au- mata (CIAA 2002) was held at the Universit ́ e Fran ̧ cois Rabelais of Tours, in Tours, France, on July 3–5, 2002. This volume of Lecture Notes in Computer Science contains all the papers that were presented at CIAA 2002, as well as the abstracts of the poster papers that were displayed during the conference. The conference addressed issues in automata application and implemen- tion. Thetopicsofthepaperspresentedinthisconferencerangedfromautomata applications in software engineering, natural language and speech recognition, and image processing, to new representations and algorithms for e?cient imp- mentation of automata and related structures. Automata theory is one of the oldest areas in computer science. Research in automata theory has always been motivated by its applications since its early stage of development. In the 1960s and 1970s, automata research was motivated heavily by problems arising from compiler construction, circuit design, string matching, etc. In recent years, many new applications of automata have been found in various areas of computer science as well as in other disciplines. - amples of the new applications include statecharts in object-oriented modeling, ?nite transducers in natural language processing, and nondeterministic ?ni- state models in communication protocols. Many of the new applications cannot simply utilize the existing models and algorithms in automata theory in the - lution to their problems. New models, or modi?cations of the existing models, are needed to satisfy their requirements.
This textbook introduces readers to the fundamental notions of modern probability theory. The only prerequisite is a working knowledge in real analysis. Highlighting the connections between martingales and Markov chains on one hand, and Brownian motion and harmonic functions on the other, this book provides an introduction to the rich interplay between probability and other areas of analysis. Arranged into three parts, the book begins with a rigorous treatment of measure theory, with applications to probability in mind. The second part of the book focuses on the basic concepts of probability theory such as random variables, independence, conditional expectation, and the different types of convergence of random variables. In the third part, in which all chapters can be read independently, the reader will encounter three important classes of stochastic processes: discrete-time martingales, countable state-space Markov chains, and Brownian motion. Each chapter ends with a selection of illuminating exercises of varying difficulty. Some basic facts from functional analysis, in particular on Hilbert and Banach spaces, are included in the appendix. Measure Theory, Probability, and Stochastic Processes is an ideal text for readers seeking a thorough understanding of basic probability theory. Students interested in learning more about Brownian motion, and other continuous-time stochastic processes, may continue reading the author’s more advanced textbook in the same series (GTM 274).
This book covers the theory of derivatives pricing and hedging as well as techniques used in mathematical finance. The authors use a top-down approach, starting with fundamentals before moving to applications, and present theoretical developments alongside various exercises, providing many examples of practical interest.A large spectrum of concepts and mathematical tools that are usually found in separate monographs are presented here. In addition to the no-arbitrage theory in full generality, this book also explores models and practical hedging and pricing issues. Fundamentals and Advanced Techniques in Derivatives Hedging further introduces advanced methods in probability and analysis, including Malliavin calculus and the theory of viscosity solutions, as well as the recent theory of stochastic targets and its use in risk management, making it the first textbook covering this topic. Graduate students in applied mathematics with an understanding of probability theory and stochastic calculus will find this book useful to gain a deeper understanding of fundamental concepts and methods in mathematical finance.
From the reviews: "This is a very interesting book containing material for a comprehensive study of the cyclid homological theory of algebras, cyclic sets and S1-spaces. Lie algebras and algebraic K-theory and an introduction to Connes'work and recent results on the Novikov conjecture. The book requires a knowledge of homological algebra and Lie algebra theory as well as basic technics coming from algebraic topology. The bibliographic comments at the end of each chapter offer good suggestions for further reading and research. The book can be strongly recommended to anybody interested in noncommutative geometry, contemporary algebraic topology and related topics." European Mathematical Society Newsletter In this second edition the authors have added a chapter 13 on MacLane (co)homology.
This will help us customize your experience to showcase the most relevant content to your age group
Please select from below
Login
Not registered?
Sign up
Already registered?
Success – Your message will goes here
We'd love to hear from you!
Thank you for visiting our website. Would you like to provide feedback on how we could improve your experience?
This site does not use any third party cookies with one exception — it uses cookies from Google to deliver its services and to analyze traffic.Learn More.