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Author Menʹshikov, M. V. (Mikhail Vasilʹevich), author.

Title Non-homogeneous random walks : Lyapunov function methods for near-critical stochastic systems / Mikhail Menshikov, University of Durham ; Serguei Popov, Universidade Estadual de Campinas, Brazil ; Andrew Wade, University of Durham
Published Cambridge : Cambridge University Press, 2017
©2017

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Description 1 online resource (xviii, 363 pages) : illustrations
Series Cambridge tracts in mathematics ; 209
Cambridge tracts in mathematics ; 209.
Contents Introduction -- Semimartingale approach and Markov chains -- Lamperti's problem -- Many-dimensional random walks -- Heavy tails -- Further applications -- Markov chains in continuous time
Summary Stochastic systems provide powerful abstract models for a variety of important real-life applications: for example, power supply, traffic flow, data transmission. They (and the real systems they model) are often subject to phase transitions, behaving in one way when a parameter is below a certain critical value, then switching behaviour as soon as that critical value is reached. In a real system, we do not necessarily have control over all the parameter values, so it is important to know how to find critical points and to understand system behaviour near these points. This book is a modern presentation of the 'semimartingale' or 'Lyapunov function' method applied to near-critical stochastic systems, exemplified by non-homogeneous random walks. Applications treat near-critical stochastic systems and range across modern probability theory from stochastic billiards models to interacting particle systems. Spatially non-homogeneous random walks are explored in depth, as they provide prototypical near-critical systems
Bibliography Includes bibliographical references and index
Notes Print version record
Subject Random walks (Mathematics)
Stochastic processes.
MATHEMATICS -- Applied.
MATHEMATICS -- Probability & Statistics -- General.
Procesos estocásticos
Random walks (Mathematics)
Stochastic processes
Genre/Form Electronic books
Form Electronic book
Author Popov, Serguei, 1972- author.
Wade, Andrew (Andrew R.), 1981- author.
ISBN 9781316868980
1316868982
9781139208468
1139208462