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A Weak Convergence Approach to the Theory of Large Deviations (Wiley Series in Probability and Statistics)
A Weak Convergence Approach to the Theory of Large Deviations (Wiley Series in Probability and Statistics) Summary:By Paul Dupuis, Richard S. Ellis
Applies the well-developed tools of the theory of weak convergence of probability measures to large deviation analysis—a consistent new approach The theory of large deviations, one of the most dynamic topics in probability today, studies rare events in stochastic systems. The nonlinear nature of the theory contributes both to its richness and difficulty. This innovative text demonstrates how to employ the well-established linear techniques of weak convergence theory to prove large deviation results. Beginning with a step-by-step development of the approach, the book skillfully guides readers through models of increasing complexity covering a wide variety of random variable-level and process-level problems. Representation formulas for large deviation-type expectations are a key tool and are developed systematically for discrete-time problems. Accessible to anyone who has a knowledge of measure theory and measure-theoretic probability, A Weak Convergence Approach to the Theory of Large Deviations is important reading for both students and researchers. From the PublisherThis book presents a new and widely applicable method to the theory of large deviations. This approach allows large deviation problems, which are nonlinear, to be reduced to problems that are essentially linear in nature (weak convergence in probability). The authors develop the weak convergence method from scratch, illustrate via several basic examples and then apply it to a number of sophisticated models. Much of the material in the text is being published for the first time. Contents: Formulation of Large Deviation Theory in Terms of the Laplace Principle. First Example: Sanov's Theorem. Second Example: Mogulskii's Theorem. Representation Formulas for Other Stochastic Processes. Compactness and Limit Properties for the Random Walk Model. Laplace Principle for the Random Walk Model with Continuous Statistics. Laplace Principle for the Random Walk Model with Discontinuous Statistics. Laplace Principle for the Empirical Measures of a Markov Chain. Extensions of the Laplace Principle for the Empirical Measures of a Markov Chain. Laplace Principle for Continuous-Time Markov Processes with Continuous Statistics. Appendices. Bibliography. Indexes. password:kodiak Please select one mirror to download
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Sponsored LinksA Weak Convergence Approach to the Theory of Large Deviations (Wiley Series in Probability and Statistics) Keywordstheory laplace weak principle convergence probability approach problems statistics deviation random deviations markov model measures theorem linear models nonlinear stochastic convergence approach complexity covering random variable level increasing complexity skillfully guides step by step development process level problems guides readers problems representation problems accessibleBookmark A Weak Convergence Approach to the Theory of Large Deviations (Wiley Series in Probability and Statistics)Hyperlink code:
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