Large deviations for stochastic processes
Series: Mathematical Surveys and Monographs Volume 131Publication details: Providence: American Mathematical Society, 2006.Description: xii, 410p.: pbk.: 25cmISBN:- 9781470418700
- 519.2 FEN
Item type | Current library | Collection | Call number | Copy number | Status | Date due | Barcode |
---|---|---|---|---|---|---|---|
Books | IIT Gandhinagar | General | 519.2 FEN (Browse shelf(Opens below)) | 1 | Available | 034081 |
Includes bibliography
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.
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