Overview

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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9781107428201

Table of Contents

Reviews

'Jinqiao Duan's book introduces the reader to the actively developing theory of stochastic dynamics through well-chosen examples that provide an overview, useful insights, and intuitive understanding of an often technically complicated topic.' P. E. Kloeden, Goethe University, Frankfurt am Main 'Randomness is an important component of modeling complex phenomena in biological, chemical, physical, and engineering systems. Based on many years teaching this material, Jinqiao Duan develops a modern approach to the fundamental theory and application of stochastic dynamical systems for applied mathematicians and quantitative engineers and scientists. The highlight is the staged development of invariant stochastic structures that underpin much of our understanding of nonlinear stochastic systems and associated properties such as escape times. The book ranges from classic Brownian motion to noise generated by -stable Levy flights.' A. J. Roberts, University of Adelaide 'This book provides a beautiful concise introduction to the flourishing field of stochastic dynamical systems, successfully integrating the exposition of important technical concepts with illustrative and insightful examples and interesting remarks regarding the simulation of such systems. Both presentation style and content are suitable for beginning graduate students in mathematics or applied mathematics who already possess an understanding of deterministic dynamical systems, as well as ordinary and partial differential equations. The book may also be of interest to applied mathematicians, as well as physicists, computer scientists and engineers who, having a sound knowledge of deterministic dynamics, wish to acquire an understanding of basic techniques for the analysis of stochastic differential equations.' Diogo Pinheiro, Mathematical Reviews Jinqiao Duan's book introduces the reader to the actively developing theory of stochastic dynamics through well-chosen examples that provide an overview, useful insights, and intuitive understanding of an often technically complicated topic. P. E. Kloeden, Goethe University, Frankfurt am Main Randomness is an important component of modeling complex phenomena in biological, chemical, physical, and engineering systems. Based on many years teaching this material, Jinqiao Duan develops a modern approach to the fundamental theory and application of stochastic dynamical systems for applied mathematicians and quantitative engineers and scientists. The highlight is the staged development of invariant stochastic structures that underpin much of our understanding of nonlinear stochastic systems and associated properties such as escape times. The book ranges from classic Brownian motion to noise generated by -stable Levy flights. A. J. Roberts, University of Adelaide This book provides a beautiful concise introduction to the flourishing field of stochastic dynamical systems, successfully integrating the exposition of important technical concepts with illustrative and insightful examples and interesting remarks regarding the simulation of such systems. Both presentation style and content are suitable for beginning graduate students in mathematics or applied mathematics who already possess an understanding of deterministic dynamical systems, as well as ordinary and partial differential equations. The book may also be of interest to applied mathematicians, as well as physicists, computer scientists and engineers who, having a sound knowledge of deterministic dynamics, wish to acquire an understanding of basic techniques for the analysis of stochastic differential equations. Diogo Pinheiro, Mathematical Reviews

Advance praise: 'Jinqiao Duan's book introduces the reader to the actively developing theory of stochastic dynamics through well-chosen examples that provide an overview, useful insights, and intuitive understanding of an often technically complicated topic.' P. E. Kloeden, Goethe University, Frankfurt am Main Advance praise: 'Randomness is an important component of modeling complex phenomena in biological, chemical, physical, and engineering systems. Based on many years teaching this material, Jinqiao Duan develops a modern approach to the fundamental theory and application of stochastic dynamical systems for applied mathematicians and quantitative engineers and scientists. The highlight is the staged development of invariant stochastic structures that underpin much of our understanding of nonlinear stochastic systems and associated properties such as escape times. The book ranges from classic Brownian motion to noise generated by alpha-stable Levy flights.' A. J. Roberts, University of Adelaide

'Jinqiao Duan's book introduces the reader to the actively developing theory of stochastic dynamics through well-chosen examples that provide an overview, useful insights, and intuitive understanding of an often technically complicated topic.' P. E. Kloeden, Goethe University, Frankfurt am Main 'Randomness is an important component of modeling complex phenomena in biological, chemical, physical, and engineering systems. Based on many years teaching this material, Jinqiao Duan develops a modern approach to the fundamental theory and application of stochastic dynamical systems for applied mathematicians and quantitative engineers and scientists. The highlight is the staged development of invariant stochastic structures that underpin much of our understanding of nonlinear stochastic systems and associated properties such as escape times. The book ranges from classic Brownian motion to noise generated by α-stable Levy flights.' A. J. Roberts, University of Adelaide 'This book provides a beautiful concise introduction to the flourishing field of stochastic dynamical systems, successfully integrating the exposition of important technical concepts with illustrative and insightful examples and interesting remarks regarding the simulation of such systems. Both presentation style and content are suitable for beginning graduate students in mathematics or applied mathematics who already possess an understanding of deterministic dynamical systems, as well as ordinary and partial differential equations. The book may also be of interest to applied mathematicians, as well as physicists, computer scientists and engineers who, having a sound knowledge of deterministic dynamics, wish to acquire an understanding of basic techniques for the analysis of stochastic differential equations.' Diogo Pinheiro, Mathematical Reviews

'Jinqiao Duan's book introduces the reader to the actively developing theory of stochastic dynamics through well-chosen examples that provide an overview, useful insights, and intuitive understanding of an often technically complicated topic.' P. E. Kloeden, Goethe University, Frankfurt am Main 'Randomness is an important component of modeling complex phenomena in biological, chemical, physical, and engineering systems. Based on many years teaching this material, Jinqiao Duan develops a modern approach to the fundamental theory and application of stochastic dynamical systems for applied mathematicians and quantitative engineers and scientists. The highlight is the staged development of invariant stochastic structures that underpin much of our understanding of nonlinear stochastic systems and associated properties such as escape times. The book ranges from classic Brownian motion to noise generated by alpha-stable Levy flights.' A. J. Roberts, University of Adelaide 'This book provides a beautiful concise introduction to the flourishing field of stochastic dynamical systems, successfully integrating the exposition of important technical concepts with illustrative and insightful examples and interesting remarks regarding the simulation of such systems. Both presentation style and content are suitable for beginning graduate students in mathematics or applied mathematics who already possess an understanding of deterministic dynamical systems, as well as ordinary and partial differential equations. The book may also be of interest to applied mathematicians, as well as physicists, computer scientists and engineers who, having a sound knowledge of deterministic dynamics, wish to acquire an understanding of basic techniques for the analysis of stochastic differential equations.' Diogo Pinheiro, Mathematical Reviews

Author Information

Before joining Great Bay University, Jinqiao Duan was Professor and Director of the Laboratory for Stochastic Dynamics at Illinois Institute of Technology. During 2011–13, 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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