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Large Deviations for Stochastic Processes

Jin Feng
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      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.
      Format: Paperback / softback CONTRIBUTORS: Jin Feng EAN: 9781470418700 COUNTRY: United States PAGES: WEIGHT: 0 g HEIGHT: 229 cm
      PUBLISHED BY: American Mathematical Society DATE PUBLISHED: 2006-12-30 CITY: GENRE: MATHEMATICS / Probability & Statistics / Stochastic Processes WIDTH: 152 cm SPINE:

      Book Themes:

      Stochastics

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      Jin Feng, University of Kansas, Lawrence, KS.Thomas G. Kurtz, University of Wisconsin at Madison, Madison, WI.
      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.
      Format: Paperback / softback CONTRIBUTORS: Jin Feng EAN: 9781470418700 COUNTRY: United States PAGES: WEIGHT: 0 g HEIGHT: 229 cm
      PUBLISHED BY: American Mathematical Society DATE PUBLISHED: 2006-12-30 CITY: GENRE: MATHEMATICS / Probability & Statistics / Stochastic Processes WIDTH: 152 cm SPINE:

      Book Themes:

      Stochastics

      Customer Reviews

      Be the first to write a review
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      Jin Feng, University of Kansas, Lawrence, KS.Thomas G. Kurtz, University of Wisconsin at Madison, Madison, WI.

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