Large Deviations (eBook)

eBook Download: PDF

1989 | 1. Auflage
306 Seiten
Elsevier Science (Verlag)
978-0-08-087457-9 (ISBN)

Infos

The first four chapters of this volume are based on lectures given by Stroock at MIT in 1987. They form an introduction to the basic ideas of the theory of large deviations and make a suitable package on which to base a semester-length course for advanced graduate students with a strong background in analysis and some probability theory. A large selection of exercises presents important material and many applications. The last two chapters present various non-uniform results (Chapter 5) and outline the analytic approach that allows one to test and compare techniques used in previous chapters (Chapter 6).

Inhalt

Front Cover 1
Large Deviations 4
Copyright Page 5
Contents 14
Chapter I: Some Examples 16
1.1: The General Idea 16
1.2: The Classical Cramèr Theorem 18
1.3: Schilder’s Theorem 23
1.4: Two Applications of Schilder’s Theorem 36
Chapter II: Some Generalities 50
2.1: The Large Deviation Principle 50
2.2: Large Deviations and Convex Analysis 67
Chapter III: Generalized Cramèr Theory 73
3.1: Preliminary Formulation 73
3.2: Sanov’s Theorem 79
3.3: Cramèr’s Theorem for Banach Spaces 93
3.4: Large Deviations for Gaussian Measures 100
Chapter IV: Uniform Large Deviations 106
4.1: Markov Chains 106
4.2: Continuous Time Markov Processes 125
4.3: The Wiener Sausage 155
4.4: Process Level Large Deviations 176
Chapter V: Non-Uniform Results 200
5.1: Generalities about the Upper Bound 200
5.2: A Little Ergodic Theory 208
5.3: The General Symmetric Markov Case 221
5.4: The Large Deviation Principle for Hypermixing Processes 228
5.5: Hypermixing in the Epsilon Markov Case 246
Chapter VI: Analytic Considerations 252
6.1: When is a Markov Process Hypermixing? 252
6.2: Symmetric Diffusions on a Manifold 265
6.3: Hypoelliptic Diffusions on a Compact Manifold 286
Historical Notes and References 299
Notation Index 316
Subject Index 320

Produkt-Details

• Erscheint lt. Verlag: 21.6.1989
• Mitarbeit: Herausgeber (Serie): Jean-Dominique Deuschel, Daniel W. Stroock
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
• Themenwelt: Technik
• ISBN-10: 0-08-087457-6 / 0080874576
• ISBN-13: 978-0-08-087457-9 / 9780080874579