Elements Of The Random Walk
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Elements Of The Random Walk
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Author : Joseph Rudnick
language : en
Publisher: Cambridge University Press
Release Date : 2010-03-25
Elements Of The Random Walk written by Joseph Rudnick 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 2010-03-25 with Science categories.
Random walks have proven to be a useful model in understanding processes across a wide spectrum of scientific disciplines. This book is an introduction to some of the most powerful and general techniques used in the application of these ideas. Its self-contained text will appeal to graduate students across science, engineering and mathematics who need to understand the applications of random walk techniques, as well as to established researchers.
Elements Of Random Walk And Diffusion Processes
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Author : Oliver C. Ibe
language : en
Publisher: John Wiley & Sons
Release Date : 2013-08-29
Elements Of Random Walk And Diffusion Processes written by Oliver C. Ibe and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-29 with Mathematics categories.
Presents an important and unique introduction to random walk theory Random walk is a stochastic process that has proven to be a useful model in understanding discrete-state discrete-time processes across a wide spectrum of scientific disciplines. Elements of Random Walk and Diffusion Processes provides an interdisciplinary approach by including numerous practical examples and exercises with real-world applications in operations research, economics, engineering, and physics. Featuring an introduction to powerful and general techniques that are used in the application of physical and dynamic processes, the book presents the connections between diffusion equations and random motion. Standard methods and applications of Brownian motion are addressed in addition to Levy motion, which has become popular in random searches in a variety of fields. The book also covers fractional calculus and introduces percolation theory and its relationship to diffusion processes. With a strong emphasis on the relationship between random walk theory and diffusion processes, Elements of Random Walk and Diffusion Processes features: Basic concepts in probability, an overview of stochastic and fractional processes, and elements of graph theory Numerous practical applications of random walk across various disciplines, including how to model stock prices and gambling, describe the statistical properties of genetic drift, and simplify the random movement of molecules in liquids and gases Examples of the real-world applicability of random walk such as node movement and node failure in wireless networking, the size of the Web in computer science, and polymers in physics Plentiful examples and exercises throughout that illustrate the solution of many practical problems Elements of Random Walk and Diffusion Processes is an ideal reference for researchers and professionals involved in operations research, economics, engineering, mathematics, and physics. The book is also an excellent textbook for upper-undergraduate and graduate level courses in probability and stochastic processes, stochastic models, random motion and Brownian theory, random walk theory, and diffusion process techniques.
Random Walks And Discrete Potential Theory
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Author : M. Picardello
language : en
Publisher: Cambridge University Press
Release Date : 1999-11-18
Random Walks And Discrete Potential Theory written by M. Picardello 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 1999-11-18 with Mathematics categories.
Comprehensive and interdisciplinary text covering the interplay between random walks and structure theory.
Aspects And Applications Of The Random Walk
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Author : George Herbert Weiss
language : en
Publisher: Elsevier Science & Technology
Release Date : 1994
Aspects And Applications Of The Random Walk written by George Herbert Weiss and has been published by Elsevier Science & Technology this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Computers categories.
Paperback. Both the formalism and many of the attendant ideas related to the random walk lie at the core of a significant fraction of contemporary research in statistical physics. In the language of physics the random walk can be described as a microscopic model for transport processes which have some element of randomness. The starting point of nearly all analyses of transport in disordered media is to be found in one or another type of random walk model. Mathematical formalism based on the theory of random walks is not only pervasive in a number of areas of physics, but also finds application in many areas of chemistry. The random walk has also been applied to the study of a number of biological phenomena.Despite the obvious importance of random walks in these and other applications there are few books devoted to the subject. This is therefore a timely introduction to the subject which will be welcomed by students and more senior researchers who have
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.
Random Walks On Infinite Groups
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Author : Steven P. Lalley
language : en
Publisher: Springer Nature
Release Date : 2023-05-08
Random Walks On Infinite Groups written by Steven P. Lalley and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-08 with Mathematics categories.
This text presents the basic theory of random walks on infinite, finitely generated groups, along with certain background material in measure-theoretic probability. The main objective is to show how structural features of a group, such as amenability/nonamenability, affect qualitative aspects of symmetric random walks on the group, such as transience/recurrence, speed, entropy, and existence or nonexistence of nonconstant, bounded harmonic functions. The book will be suitable as a textbook for beginning graduate-level courses or independent study by graduate students and advanced undergraduate students in mathematics with a solid grounding in measure theory and a basic familiarity with the elements of group theory. The first seven chapters could also be used as the basis for a short course covering the main results regarding transience/recurrence, decay of return probabilities, and speed. The book has been organized and written so as to be accessible not only to students in probability theory, but also to students whose primary interests are in geometry, ergodic theory, or geometric group theory.
Random Walks With Ordered Elements
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Author : Gunnar Blom
language : en
Publisher:
Release Date : 1984
Random Walks With Ordered Elements written by Gunnar Blom and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with categories.
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.
Random Walk In Random And Non Random Environments
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Author : P l Rvsz
language : en
Publisher: World Scientific
Release Date : 2013
Random Walk In Random And Non Random Environments written by P l Rvsz 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 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 OCo 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.
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.