Jinqiao (Jeffrey) Duan, professor of applied mathematics, has written a new book, An Introduction to Stochastic Dynamics, to be published by Cambridge University Press in November 2014.
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, nano composites, and communication systems.
An Introduction to Stochastic Dynamics is an accessible summary for understanding dynamical systems under random influences, important for everything from forecasting the weather to anticipating earthquakes to avoiding financial meltdowns. It is ideal for professionals in quantitative finance and national laboratories as well as for academic researchers and graduate students in applied mathematics, engineering, and science.
Dynamical systems often are subject to external fluctuations, internal agitation, fluctuating initial conditions, and uncertain parameters. The uncertainty, or randomness, may have a delicate and profound impact on the overall evolution of complex dynamical systems. What are those impacts? How can we quantify uncertainty and systemic risks in stochastic dynamical systems? How reliable are mechanical/electronic or any other man-made systems when random fluctuations are not taken into account? How can we take advantage of or mitigate the influences of noise?
An Introduction to Stochastic Dynamics answers these questions. 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.
Duan is Director of the Laboratory for Stochastic Dynamics at Illinois Institute of Technology. From 2011-2013, 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 the research monograph Effective Dynamics of Stochastic Partial Differential Equations (Elsevier, 2014). He is a member of the Society for Industrial and Applied Mathematics (SIAM).