Non-homogeneous Random Walks

Lyapunov Function Methods for Near-Critical Stochastic Systems

Nonfiction, Science & Nature, Mathematics, Group Theory, Statistics
Cover of the book Non-homogeneous Random Walks by Mikhail Menshikov, Serguei Popov, Andrew Wade, Cambridge University Press
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Author: Mikhail Menshikov, Serguei Popov, Andrew Wade ISBN: 9781316866825
Publisher: Cambridge University Press Publication: December 22, 2016
Imprint: Cambridge University Press Language: English
Author: Mikhail Menshikov, Serguei Popov, Andrew Wade
ISBN: 9781316866825
Publisher: Cambridge University Press
Publication: December 22, 2016
Imprint: Cambridge University Press
Language: English

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.

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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.

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