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Type of bind: Hardcover
Dewey Decimal Number: 519.2
EAN num: 9780821841457
ISBN number: 0821841459
Label: American Mathematical Society
Manufacturer: American Mathematical Society
Quantity: 1
Page Count: 410
Printing Date: October 31, 2006
Publishing house: American Mathematical Society
Release Date: October 31, 2006
Sale Popularity Level: 1976539
Studio: American Mathematical Society
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Product Description:
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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