Random Ordinary Differential Equations and Their Numerical Solution (Probability Theory and Stochastic Modelling, 85)

This book is intended to make recent results on the derivation of higher order numerical schemes for random ordinary differential equations (RODEs) available to a broader readership, and to familiarize readers with RODEs themselves as well as the closely associated theory of random dynamical systems. In addition, it demonstrates how RODEs are being used in the biological sciences, where non-Gaussian and bounded noise are often more realistic than the Gaussian white noise in stochastic differential equations (SODEs).

The book is directed at a wide range of readers in applied and computational mathematics and related areas as well as readers who are interested in the applications of mathematical models involving random effects, in particular in the biological sciences.The level of this book is suitable for graduate students in applied mathematics and related areas, computational sciences and systems biology.  A basic knowledge of ordinary differential equations and numerical analysis is required. 

Professor Xiaoying Han’s main research interests are in random and nonautonomous dynamical systems and their applications.  In addition to mathematical analysis of dynamical systems, she is also interested in modeling and simulation of applied dynamical systems in biology, chemical engineering, ecology, material sciences, etc.  She is the coauthor of the books “Applied Nonautonomous and Random Dynamical Systems” (with T. Caraballo) and “Attractors under Discretisation” (with P. E. Kloeden), published in the SpringerBrief series.