Transcription of Lectures on the Large Deviation Principle
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Lectures on the Large Deviation Principle Fraydoun Rezakhanlou . Department of Mathematics, UC Berkeley March 25, 2017.. This work is supported in part by NSF grant DMS-1407723. 1. Chapter 1: Introduction Chapter 2: A General Strategy Chapter 3: Crame r and Sanov Large Deviation Principles Chapter 4: Donsker-Varadhan Theory Chapter 5: Large Deviation Principles for Markov Chains Chapter 6: Wentzell-Freidlin Problem Chapter 7: stochastic Calculus and Martingale Problem Chapter 8: Miscellaneous Appendix A: Probability Measures on Polish Spaces Appendix B: Conditional Measures Appendix C: Ergodic Theorem Appendix D: Minimax Principle Appendix E: Optimal Transport Problem 2. 1 Introduction Many questions in probability theory can be formulated as a law of Large numbers (LLN).
This is Schilder’s LDP and its generalization to general stochastic di erential equations (SDE) is the cornerstone of the Wentzell-Freidlin Theory. Roughly, if x " solves
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