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  Manydimensional random walks  Heavy tails  Further applications  Markov chains in continuous time 
Summary 
Stochastic systems provide powerful abstract models for a variety of important reallife 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 nearcritical stochastic systems, exemplified by nonhomogeneous random walks. Applications treat nearcritical stochastic systems and range across modern probability theory from stochastic billiards models to interacting particle systems. Spatially nonhomogeneous random walks are explored in depth, as they provide prototypical nearcritical 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 
