Applied Stochastic Processes and Control for Jump Diffusions

This self-contained, practical, entry-level text integrates the basic principles of applied mathematics, applied probability, and computational science for a clear presentation of stochastic processes and control for jump-diffusions in continuous time.

The author covers the important problem of controlling these systems and, through the use of a jump calculus construction, discusses the strong role of discontinuous and nonsmooth properties versus random properties in stochastic systems. The book emphasises modelling and problem solving and presents sample applications in financial engineering and biomedical modelling.

Computational and analytic exercises and examples are included throughout. While classical applied mathematics is used in most of the chapters to set up systematic derivations and essential proofs, the final chapter bridges the gap between the applied and the abstract worlds to give readers an understanding of the more abstract literature on jump-diffusions.

An additional 160 pages of online appendices are available on a Web page that supplements the book.

This book is written for graduate students in science and engineering who seek to construct models for scientific applications subject to uncertain environments. Mathematical modellers and researchers in applied mathematics, computational science, and engineering will also find it useful, as will practitioners of financial engineering who need fast and efficient solutions to stochastic problems.

About the Author

Floyd B. Hanson is Professor Emeritus in the Department of Mathematics, Statistics, and Computer Science at the University of Illinois, Chicago. He received the Premier UIC Award for Excellence in Teaching for 2001 and has published approximately 100 research papers.