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.

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'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

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