{"product_id":"large-deviations-for-stochastic-processes","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":"American Mathematical Society","offers":[{"title":"Default Title","offer_id":56628415758680,"sku":"9781470418700","price":122.99,"currency_code":"EUR","in_stock":true}],"url":"https:\/\/agendabookshop.com\/products\/large-deviations-for-stochastic-processes","provider":"Agenda Bookshop","version":"1.0","type":"link"}