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An accessible introduction for applied mathematicians to concepts and techniques for describing, quantifying, and understanding dynamics under uncertainty.
List of contents
1. Introduction; 2. Background in analysis and probability; 3. Noise; 4. A crash course in stochastic differential equations; 5. Deterministic quantities for stochastic dynamics; 6. Invariant structures for stochastic dynamics; 7. Dynamical systems driven by non-Gaussian Lévy motions.
About the author
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.
Summary
This book serves as a concise introductory text on stochastic dynamics for applied mathematicians. Rich with examples, illustrations, and exercises with their solutions, it provides an accessible introduction to concepts and techniques for describing, quantifying, and understanding dynamics under uncertainty, from analytical, deterministic, structural and numerical perspectives.
