Large Deviations for Stochastic Processes (Mathematical Surveys and Monographs, 131) - Softcover

Jin Feng; Thomas G. Kurtz

Softcover

ISBN 10: 1470418703 ISBN 13: 9781470418700

Publisher: American Mathematical Society, 2015

Synopsis

The book is devoted to the results on large deviations for a class of stochastic processes. Following an introduction and overview, the material is presented in three parts. Part 1 gives necessary and sufficient conditions for exponential tightness that are analogous to conditions for tightness in the theory of weak convergence. Part 2 focuses on Markov processes in metric spaces. For a sequence of such processes, convergence of Fleming's logarithmically transformed nonlinear semigroups is shown to imply the large deviation principle in a manner analogous to the use of convergence of linear semigroups in weak convergence. Viscosity solution methods provide applicable conditions for the necessary convergence. Part 3 discusses methods for verifying the comparison principle for viscosity solutions and applies the general theory to obtain a variety of new and known results on large deviations for Markov processes. In examples concerning infinite dimensional state spaces, new comparison principles are derived for a class of Hamilton-Jacobi equations in Hilbert spaces and in spaces of probability measures.

About this title

About the Author

Jin Feng: University of Kansas, Lawrence, KS, Thomas G. Kurtz: University of Wisconsin at Madison, Madison, WI

Edition details

• Publisher: American Mathematical Society
• Publication date: 2015
• Language: English
• ISBN 10: 1470418703
• ISBN 13: 9781470418700
• Binding: Paperback
• Number of pages: 401