Large Deviations for Stochastic Processes - Brossura

Feng, Jin; Kurtz, Thomas G.

Brossura

ISBN 10: 1470418703 ISBN 13: 9781470418700

Casa editrice: Amer Mathematical Society, 2006

Riassunto

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.

Dettagli dell'edizione

• Editore: Amer Mathematical Society
• Data di pubblicazione: 2006
• Lingua: Inglese
• ISBN 10: 1470418703
• ISBN 13: 9781470418700
• Rilegatura: Copertina flessibile
• Numero di pagine: 410
• Contatto del produttore: non disponibile
• Persona responsabile: Mare Nostrum Group B.V.; gpsr@mare-nostrum.co.uk; ; Doelen 72; Breda; 4831 GR; Paesi Bassi