Large Deviations And Idempotent Probability
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Large Deviations and Idempotent Probability
In the view of many probabilists, author Anatolii Puhalskii's research results stand among the most significant achievements in the modern theory of large deviations. In fact, his work marked a turning point in the depth of our understanding of the connections between the large deviation principle (LDP) and well-known methods for establishing weak
Large Deviations for Stochastic Processes
Author: Jin Feng
language: en
Publisher: American Mathematical Soc.
Release Date: 2015-02-03
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.
Decision Theory and Multi-Agent Planning
Author: Giacomo Della Riccia
language: en
Publisher: Springer Science & Business Media
Release Date: 2007-05-03
The work presents a modern, unified view on decision support and planning by considering its basics like preferences, belief, possibility and probability as well as utilities. These features together are immanent for software agents to believe the user that the agents are "intelligent".