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基本説明
Divided into two parts: theory and applications. Basic large deviation theorems are presented for i.i.d. sequences, Markov sequences, and sequences with moderate dependence.
Full Description
This volume offers an introduction to large deviations. It is divided into two parts: theory and applications. Basic large deviation theorems are presented for i.i.d. sequences, Markov sequences, and sequences with moderate dependence. The rate function is computed explicitly. The theory is explained without too much emphasis on technicalities. Also included is an outline of general definitions and theorems. The goal is to expose the unified theme that gives large deviation theory its overall structure, which can be made to work in many concrete cases. The section on applications focuses on recent work in statistical physics and random media. This book contains 60 exercises (with solutions) that should elucidate the content and engage the reader. Prerequisites for the book are a strong background in probability and analysis and some knowledge of statistical physics. It would make an excellent textbook for a special topics course in large deviations.
Contents
Theory: Large deviations for i.i.d. sequences: Part 1 Large deviations for i.i.d. sequences: Part 2 General theory Large deviations for Markov sequences Large deviations for dependent sequences Applications: Statistical hypothesis testing Random walk in random environment Heat conduction with random sources and sinks Polymer chains Interacting diffusions Solutions to the exercises Bibliography Index Glossary of symbols Errata.
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