bokomslag Large Deviations for Stochastic Processes
Vetenskap & teknik

Large Deviations for Stochastic Processes

Jin Feng Thomas G Kurtz

Pocket

2179:-

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  • 410 sidor
  • 2006
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.
  • Författare: Jin Feng, Thomas G Kurtz
  • Format: Pocket/Paperback
  • ISBN: 9781470418700
  • Språk: Engelska
  • Antal sidor: 410
  • Utgivningsdatum: 2006-12-01
  • Förlag: American Mathematical Society