An Introduction to Stochastic Dynamics

Front Cover
Cambridge University Press, Apr 13, 2015 - Mathematics - 291 pages
The mathematical theory of stochastic dynamics has become an important tool in the modeling of uncertainty in many complex biological, physical, and chemical systems and in engineering applications - for example, gene regulation systems, neuronal networks, geophysical flows, climate dynamics, chemical reaction systems, nanocomposites, and communication systems. It is now understood that these systems are often subject to random influences, which can significantly impact their evolution. This book serves as a concise introductory text on stochastic dynamics for applied mathematicians and scientists. Starting from the knowledge base typical for beginning graduate students in applied mathematics, it introduces the basic tools from probability and analysis and then develops for stochastic systems the properties traditionally calculated for deterministic systems. The book's final chapter opens the door to modeling in non-Gaussian situations, typical of many real-world applications. Rich with examples, illustrations, and exercises with solutions, this book is also ideal for self-study.
 

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Contents

Introduction
1
Background in Analysis and Probability
12
Noise
59
A Crash Course in Stochastic Differential Equations
61
2
65
1
77
22
85
Deterministic Quantities for Stochastic Dynamics
99
35
108
Invariant Structures for Stochastic Dynamics
133
Dynamical Systems Driven by NonGaussian Levy Motions
188
Hints and Solutions
245
Further Readings
271
Index
287
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About the author (2015)

Jinqiao Duan is Professor and Director of the Laboratory for Stochastic Dynamics at Illinois Institute of Technology. During 2011 3, he also served as Professor and Associate Director of the Institute for Pure and Applied Mathematics (IPAM) at the University of California, Los Angeles. An expert in stochastic dynamics, stochastic partial differential equations, and their applications in engineering and science, he has been the managing editor for the journal Stochastics and Dynamics for over a decade. He is also a co-author of a research monograph, Effective Dynamics of Stochastic Partial Differential Equations (2014), based on his teaching at various universities since 1997.

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