Preface Chapter 1 Some Examples 1.1 The General Idea 1.2 The Classical Cram?r Theorem 1.3 Schilder's Theorem 1.4 Two Applications of Schilder's Theorem Chapter 2 Some Generalities 2.1 The Large Deviation Principle 2.2 Large Deviations and Convex Analysis Chapter 3 General Cram?r Theory 3.1 Preliminary Formulation 3.2 Sanov's Theorem 3.3 Cram?r's Theorem 3.4 Large Deviations for Banach Spaces 3.5 Large Deviations for Gaussian Measures Chapter 4 Uniform Large Deviations 4.1 Markov Chains 4.2 Continuous Time Markov Processes 4.3 The Wiener Sausage 4.4 Process Level Large Deviations Chapter 5 Non - Uniform Results 5.1 Generalities about the Upper Bound 5.2 A Little Ergodic Theory 5.3 The General Symmetric Markov Case 5.4 Large Deviations for Hypermixing Processes 5.5 Hypermixing in the Epsilon Markov Case Chapter 6 Analytic Considerations 6.1 When Is a Markov Process Hypermixing? 6.2 Symmetric Diffusions on a Manifold 6.3 Hypoelliptic Diffusions on a Compact Manifold Historical Notes and References Name Index Bibliography Frequently Used Notation Index
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