Random Walk In Random And Non Random Environments Third Edition
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Random Walk In Random And Non Random Environments Third Edition
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Author : Revesz Pal
language : en
Publisher: World Scientific
Release Date : 2013-03-06
Random Walk In Random And Non Random Environments Third Edition written by Revesz Pal and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-06 with Mathematics categories.
The simplest mathematical model of the Brownian motion of physics is the simple, symmetric random walk. This book collects and compares current results — mostly strong theorems which describe the properties of a random walk. The modern problems of the limit theorems of probability theory are treated in the simple case of coin tossing. Taking advantage of this simplicity, the reader is familiarized with limit theorems (especially strong ones) without the burden of technical tools and difficulties. An easy way of considering the Wiener process is also given, through the study of the random walk.Since the first and second editions were published in 1990 and 2005, a number of new results have appeared in the literature. The first two editions contained many unsolved problems and conjectures which have since been settled; this third, revised and enlarged edition includes those new results. In this edition, a completely new part is included concerning Simple Random Walks on Graphs. Properties of random walks on several concrete graphs have been studied in the last decade. Some of the obtained results are also presented.
Random Walk In Random And Non Random Environments Second Edition
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Author : Revesz Pal
language : en
Publisher: World Scientific
Release Date : 2005-08-11
Random Walk In Random And Non Random Environments Second Edition written by Revesz Pal and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-11 with Mathematics categories.
The simplest mathematical model of the Brownian motion of physics is the simple, symmetric random walk. This book collects and compares current results — mostly strong theorems which describe the properties of a random walk. The modern problems of the limit theorems of probability theory are treated in the simple case of coin tossing. Taking advantage of this simplicity, the reader is familiarized with limit theorems (especially strong ones) without the burden of technical tools and difficulties. An easy way of considering the Wiener process is also given, through the study of the random walk.Since the first edition was published in 1990, a number of new results have appeared in the literature. The original edition contained many unsolved problems and conjectures which have since been settled; this second revised and enlarged edition includes those new results. Three new chapters have been added: frequently and rarely visited points, heavy points and long excursions. This new edition presents the most complete study of, and the most elementary way to study, the path properties of the Brownian motion.
Random Walks Of Infinitely Many Particles
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Author : Pal Revesz
language : en
Publisher: World Scientific
Release Date : 1994-09-12
Random Walks Of Infinitely Many Particles written by Pal Revesz and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-09-12 with Mathematics categories.
The author's previous book, Random Walk in Random and Non-Random Environments, was devoted to the investigation of the Brownian motion of a simple particle. The present book studies the independent motions of infinitely many particles in the d-dimensional Euclidean space Rd. In Part I the particles at time t = 0 are distributed in Rd according to the law of a given random field and they execute independent random walks. Part II is devoted to branching random walks, i.e. to the case where the particles execute random motions and birth and death processes independently. Finally, in Part III, functional laws of iterated logarithms are proved for the cases of independent motions and branching processes.
Stochastic Processes
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Author : Andrei N Borodin
language : en
Publisher: Birkhäuser
Release Date : 2017-10-30
Stochastic Processes written by Andrei N Borodin and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-30 with Mathematics categories.
This book provides a rigorous yet accessible introduction to the theory of stochastic processes. A significant part of the book is devoted to the classic theory of stochastic processes. In turn, it also presents proofs of well-known results, sometimes together with new approaches. Moreover, the book explores topics not previously covered elsewhere, such as distributions of functionals of diffusions stopped at different random times, the Brownian local time, diffusions with jumps, and an invariance principle for random walks and local times. Supported by carefully selected material, the book showcases a wealth of examples that demonstrate how to solve concrete problems by applying theoretical results. It addresses a broad range of applications, focusing on concrete computational techniques rather than on abstract theory. The content presented here is largely self-contained, making it suitable for researchers and graduate students alike.
Random Walk A Modern Introduction
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Author : Gregory F. Lawler
language : en
Publisher: Cambridge University Press
Release Date : 2010-06-24
Random Walk A Modern Introduction written by Gregory F. Lawler and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-24 with Mathematics categories.
Random walks are stochastic processes formed by successive summation of independent, identically distributed random variables and are one of the most studied topics in probability theory. This contemporary introduction evolved from courses taught at Cornell University and the University of Chicago by the first author, who is one of the most highly regarded researchers in the field of stochastic processes. This text meets the need for a modern reference to the detailed properties of an important class of random walks on the integer lattice. It is suitable for probabilists, mathematicians working in related fields, and for researchers in other disciplines who use random walks in modeling.
Probability Theory
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Author : Werner Linde
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2024-06-04
Probability Theory written by Werner Linde and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-04 with Mathematics categories.
This book is intended as an introduction to Probability Theory and Mathematical Statistics for students in mathematics, the physical sciences, engineering, and related fields. It is based on the author’s 25 years of experience teaching probability and is squarely aimed at helping students overcome common difficulties in learning the subject. The focus of the book is an explanation of the theory, mainly by the use of many examples. Whenever possible, proofs of stated results are provided. All sections conclude with a short list of problems. The book also includes several optional sections on more advanced topics. This textbook would be ideal for use in a first course in Probability Theory. Contents: Probabilities Conditional Probabilities and Independence Random Variables and Their Distribution Operations on Random Variables Expected Value, Variance, and Covariance Normally Distributed Random Vectors Limit Theorems Introduction to Stochastic Processes Mathematical Statistics Appendix Bibliography Index
Random Walks And Random Environments
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Author : Barry D. Hughes
language : en
Publisher:
Release Date : 2023
Random Walks And Random Environments written by Barry D. Hughes and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with Mathematical physics categories.
Intersections Of Random Walks
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Author : Gregory F. Lawler
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Intersections Of Random Walks written by Gregory F. Lawler and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
A more accurate title for this book would be "Problems dealing with the non-intersection of paths of random walks. " These include: harmonic measure, which can be considered as a problem of nonintersection of a random walk with a fixed set; the probability that the paths of independent random walks do not intersect; and self-avoiding walks, i. e. , random walks which have no self-intersections. The prerequisite is a standard measure theoretic course in probability including martingales and Brownian motion. The first chapter develops the facts about simple random walk that will be needed. The discussion is self-contained although some previous expo sure to random walks would be helpful. Many of the results are standard, and I have made borrowed from a number of sources, especially the ex cellent book of Spitzer [65]. For the sake of simplicity I have restricted the discussion to simple random walk. Of course, many of the results hold equally well for more general walks. For example, the local central limit theorem can be proved for any random walk whose increments have mean zero and finite variance. Some of the later results, especially in Section 1. 7, have not been proved for very general classes of walks. The proofs here rely heavily on the fact that the increments of simple random walk are bounded and symmetric.
Lectures On Probability Theory And Statistics
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Author : Amir Dembo
language : en
Publisher: Springer
Release Date : 2005-11-27
Lectures On Probability Theory And Statistics written by Amir Dembo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-27 with Mathematics categories.
This volume contains two of the three lectures that were given at the 33rd Probability Summer School in Saint-Flour (July 6-23, 2003). Amir Dembo’s course is devoted to recent studies of the fractal nature of random sets, focusing on some fine properties of the sample path of random walk and Brownian motion. In particular, the cover time for Markov chains, the dimension of discrete limsup random fractals, the multi-scale truncated second moment and the Ciesielski-Taylor identities are explored. Tadahisa Funaki’s course reviews recent developments of the mathematical theory on stochastic interface models, mostly on the so-called \nabla \varphi interface model. The results are formulated as classical limit theorems in probability theory, and the text serves with good applications of basic probability techniques.
Principles Of Random Walk
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Author : Frank Spitzer
language : en
Publisher: Springer Science & Business Media
Release Date : 2001
Principles Of Random Walk written by Frank Spitzer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
More than 100 pages of examples and problems illustrate and clarify the presentation."--BOOK JACKET.