{"product_id":"a-weak-convergence-approach-to-the-theory-of-large-deviations-hardback-9780471076728","title":"A Weak Convergence Approach to the Theory of Large Deviations (Hardback) 9780471076728","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eA Weak Convergence Approach to the Theory of Large Deviations\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003ePaul Dupuis (Author), Richard S. Ellis (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780471076728, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 10 March 1997\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e504 pages\u003cbr\u003e24 x 16.5 x 2.8 cm, 0.879 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eApplies the well-developed tools of the theory of weak convergenceof probability measures to large deviation analysis--a consistentnew approach\u003cbr\u003e \u003cbr\u003e The theory of large deviations, one of the most dynamic topics inprobability today, studies rare events in stochastic systems. Thenonlinear nature of the theory contributes both to its richness anddifficulty. This innovative text demonstrates how to employ thewell-established linear techniques of weak convergence theory toprove large deviation results. Beginning with a step-by-stepdevelopment of the approach, the book skillfully guides readersthrough models of increasing complexity covering a wide variety ofrandom variable-level and process-level problems. Representationformulas for large deviation-type expectations are a key tool andare developed systematically for discrete-time problems.\u003cbr\u003e \u003cbr\u003e Accessible to anyone who has a knowledge of measure theory andmeasure-theoretic probability, A Weak Convergence Approach to theTheory of Large Deviations is important reading for both studentsand researchers.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eFormulation of Large Deviation Theory in Terms of the LaplacePrinciple.\u003cbr\u003e \u003cbr\u003e First Example: Sanov's Theorem.\u003cbr\u003e \u003cbr\u003e Second Example: Mogulskii's Theorem.\u003cbr\u003e \u003cbr\u003e Representation Formulas for Other Stochastic Processes.\u003cbr\u003e \u003cbr\u003e Compactness and Limit Properties for the Random Walk Model.\u003cbr\u003e \u003cbr\u003e Laplace Principle for the Random Walk Model with ContinuousStatistics.\u003cbr\u003e \u003cbr\u003e Laplace Principle for the Random Walk Model with DiscontinuousStatistics.\u003cbr\u003e \u003cbr\u003e Laplace Principle for the Empirical Measures of a MarkovChain.\u003cbr\u003e \u003cbr\u003e Extensions of the Laplace Principle for the Empirical Measures of aMarkov Chain.\u003cbr\u003e \u003cbr\u003e Laplace Principle for Continuous-Time Markov Processes withContinuous Statistics.\u003cbr\u003e \u003cbr\u003e Appendices.\u003cbr\u003e \u003cbr\u003e Bibliography.\u003cbr\u003e \u003cbr\u003e Indexes.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Wiley-Interscience","offers":[{"title":"Brand New","offer_id":52278197453080,"sku":"9780471076728","price":136.39,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9780471076728.jpg?v=1781459674","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/a-weak-convergence-approach-to-the-theory-of-large-deviations-hardback-9780471076728","provider":"Freshly Printed Books","version":"1.0","type":"link"}