An Introduction to Stochastic Dynamics

An accessible introduction for applied mathematicians to concepts and techniques for describing, quantifying, and understanding dynamics under uncertainty.

Jinqiao Duan (Author)

9781107075399, Cambridge University Press

Hardback, published 13 April 2015

312 pages, 60 b/w illus. 100 exercises
24.4 x 1.9 x 17 cm, 0.7 kg

'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

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.

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.

Subject Areas: Stochastics [PBWL], Mathematical modelling [PBWH], Applied mathematics [PBW], Probability & statistics [PBT]