Vladimir Uchaikin's Books

Chance and Stability

Stable Distributions and Their Applications

By: Vladimir Vasilʹevich Uchaĭkin,Vladimir Michajlovič Zolotarev

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Chance and Stability

Stable Distributions and Their Applications

By: Vladimir Vasilʹevich Uchaĭkin,Vladimir Michajlovič Zolotarev

The series is devoted to the publication of high-level monographs and surveys which cover the whole spectrum of probability and statistics. The books of the series are addressed to both experts and advanced students.

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Page Count

606

Publisher

VSP

Published Date

ISBN 10

9067643017

ISBN 13

9789067643016

Fractional Kinetics in Solids

Anomalous Charge Transport in Semiconductors, Dielectrics, and Nanosystems

By: Vladimir Vasilʹevich Uchaĭkin,Renat Sibatov

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Fractional Kinetics in Solids

Anomalous Charge Transport in Semiconductors, Dielectrics, and Nanosystems

By: Vladimir Vasilʹevich Uchaĭkin,Renat Sibatov

The standard (Markovian) transport model based on the Boltzmann equation cannot describe some non-equilibrium processes called anomalous that take place in many disordered solids. Causes of anomality lie in non-uniformly scaled (fractal) spatial heterogeneities, in which particle trajectories take cluster form. Furthermore, particles can be located in some domains of small sizes (traps) for a long time. Estimations show that path length and waiting time distributions are often characterized by heavy tails of the power law type. This behavior allows the introduction of time and space derivatives of fractional orders. Distinction of path length distribution from exponential is interpreted as a consequence of media fractality, and analogous property of waiting time distribution as a presence of memory. In this book, a novel approach using equations with derivatives of fractional orders is applied to describe anomalous transport and relaxation in disordered semiconductors, dielectrics and quantum dot systems. A relationship between the self-similarity of transport, the Levy stable limiting distributions and the kinetic equations with fractional derivatives is established. It is shown that unlike the well-known Scher Montroll and Arkhipov Rudenko models, which are in a sense alternatives to the normal transport model, fractional differential equations provide a unified mathematical framework for describing normal and dispersive transport. The fractional differential formalism allows the equations of bipolar transport to be written down and transport in distributed dispersion systems to be described. The relationship between fractional transport equations and the generalized limit theorem reveals the probabilistic aspects of the phenomenon in which a dispersive to Gaussian transport transition occurs in a time-of-flight experiment as the applied voltage is decreased and/or the sample thickness increased. Recent experiments devoted to studies of transport in quantum dot arrays are discussed in the framework of dispersive transport models. The memory phenomena in systems under consideration are discussed in the analysis of fractional equations. It is shown that the approach based on the anomalous transport models and the fractional kinetic equations may be very useful in some problems that involve nano-sized systems. These are photon counting statistics of blinking single quantum dot fluorescence, relaxation of current in colloidal quantum dot arrays, and some others.

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Page Count

274

Publisher

World Scientific

Published Date

ISBN 10

9814355429

ISBN 13

9789814355421

Generalized Poisson Models and Their Applications in Insurance and Finance

By: Vladimir E. Bening,Victor Yu Korolev

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Generalized Poisson Models and Their Applications in Insurance and Finance

By: Vladimir E. Bening,Victor Yu Korolev

This volume in the "Modern Probability and Statistics series aims to fill the gap in existing literature on compound Cox processes, i.e. sums of independent identically distributed random variables up to a doubly stochastic Poisson process, which are very important, especially for insurance and financial applications where they provide good asymptotic approximations for basic characteristics such as the distributions of the surplus of an insurance company under risk and portfolio fluctuations or of increments of stock prices under non-constant intensity of trade. It presents the present state-of-the-art in the field of compound Cox processes and their applications in insurance and finance. Besides a review of well-known classical results on compound and mixed Poisson processes and risk theory, it contains many new, recently obtained results by the authors. Among these are: new convergence criteria, convergence rate estimates, asymptotic expansions for quantiles of stochastic processes and many others. From the applied problems considered in this book, four deserve to be mentioned especially: 1) modelling the distribution of increments of stock prices, closely connected with prediction of the behaviour of financial indexes; 2) the description of asymptotic behaviour of the so-called generalized risk processes, which take into account both risk and portfolio fluctuations; 3) statistical estimation of the probability of ruin for a generalized risk process; 4) construction of refined approximations to the ruin probability, based on its asymptotic expansions with small safety loading. This book will be of great value to specialists in applied probability and to those who use modelsand methods of probability theory to solve practical problems in the fields of insurance and finance.

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Page Count

464

Publisher

VSP

Published Date

ISBN 10

9067643661

ISBN 13

9789067643665

Fractional Kinetics in Solids

Anomalous Charge Transport in Semiconductors, Dielectrics, and Nanosystems

By: Vladimir Vasilʹevich Uchaĭkin,Renat Sibatov

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Fractional Kinetics in Solids

Anomalous Charge Transport in Semiconductors, Dielectrics, and Nanosystems

By: Vladimir Vasilʹevich Uchaĭkin,Renat Sibatov

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Page Count

274

Publisher

World Scientific

Published Date

ISBN 10

9814355429

ISBN 13

9789814355421

Fractional Kinetics In Space: Anomalous Transport Models

By: Vladimir V Uchaikin,Renat T Sibatov

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Fractional Kinetics In Space: Anomalous Transport Models

By: Vladimir V Uchaikin,Renat T Sibatov

This book is first of its kind describing a new direction in modeling processes taking place in interplanetary and interstellar space (magnetic fields, plasma, cosmic rays, etc.). This method is based on a special mathematical analysis — fractional calculus. The reader will find in this book clear physical explanation of the fractional approach and will become familiar with basic rules in this calculus and main results obtained in frame of this approach. In spite of its profound subject, the book is not overloaded by mathematical details. It contains many illustrations, rich citation and remains accessible to a wide circle of physicists.This book is addressed to graduate and postgraduate students, young and mature researchers specializing in applications of fractional calculus, astrophysics, solar-terrestrial science and physics of cosmic rays.

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Page Count

300

Publisher

World Scientific

Published Date

ISBN 10

9813225440

ISBN 13

9789813225442

Book's by Vladimir Uchaikin

Chance and Stability

Chance and Stability

Fractional Kinetics in Solids

Fractional Kinetics in Solids

Generalized Poisson Models and Their Applications in Insurance and Finance

Generalized Poisson Models and Their Applications in Insurance and Finance

Fractional Kinetics in Solids

Fractional Kinetics in Solids

Fractional Kinetics In Space: Anomalous Transport Models

Fractional Kinetics In Space: Anomalous Transport Models

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