{"product_id":"9781470418700","title":"Large Deviations for Stochastic Processes","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.","brand":"Jin Feng","offers":[{"title":"Default Title","offer_id":46776513790270,"sku":"9781470418700","price":0.0,"currency_code":"ZAR","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4357\/7662\/products\/9781470418700_87c44158-0baf-420a-9cf8-626ee2e34d83.jpg?v=1707476974","url":"https:\/\/exclusivebooks.co.za\/products\/9781470418700","provider":"Exclusive Books Online","version":"1.0","type":"link"}