Large deviations techniques and applications:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
New York [u.a.]
Springer
1998
|
| Edition: | 2. ed. |
| Series: | Applications of mathematics
38 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 363 - 384 |
| Physical Description: | XVI, 396 S. graph. Darst. |
| ISBN: | 0387984062 |
Staff View
MARC
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| 100 | 1 | |a Dembo, Amir |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Large deviations techniques and applications |c Amir Dembo ; Ofer Zeitouni |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 1998 | |
| 300 | |a XVI, 396 S. |b graph. Darst. | ||
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| 490 | 1 | |a Applications of mathematics |v 38 | |
| 500 | |a Literaturverz. S. 363 - 384 | ||
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Record in the Search Index
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| adam_text | Contents
Preface to the Second Edition vii
Preface to the First Edition ix
1 Introduction 1
1.1 Rare Events and Large Deviations 1
1.2 The Large Deviation Principle 4
1.3 Historical Notes and References 9
2 LDP for Finite Dimensional Spaces 11
2.1 Combinatorial Techniques for Finite Alphabets 11
2.1.1 The Method of Types and Sanov s Theorem 12
2.1.2 CrameVs Theorem for Finite Alphabets in K .... 18
2.1.3 Large Deviations for Sampling Without Replacement 20
2.2 CrameVs Theorem 26
2.2.1 CrameVs Theorem in 1R 26
2.2.2 CrameVs Theorem in Hld 36
2.3 The Gärtner Ellis Theorem 43
2.4 Concentration Inequalities 55
2.4.1 Inequalities for Bounded Martingale Differencea ... 55
2.4.2 Talagrand s Concentration Inequalities 60
2.5 Historical Notes and References • • 68
xiii
xiv Contents
3 Applications—The Finite Dimensional Case 71
3.1 Large Deviations for Finite State Markov Chains 72
3.1.1 LDP for Additive Functionals of Markov Chains . . 73
3.1.2 Sanov s Theorem for the Empirical Measure of Markov
Chains 76
3.1.3 Sanov s Theorem for the Pair Empirical Measure of
Markov Chains 78
3.2 Long Rare Segments in Random Walks 82
3.3 The Gibbs Conditioning Principle for Finite Alphabets ... 87
3.4 The Hypothesis Testing Problem 90
3.5 Generalized Likelihood Ratio Test for Finite Alphabets . . 96
3.6 Rate Distortion Theory 101
3.7 Moderate Deviations and Exact Asymptotics in lRd 108
3.8 Historical Notes and References 113
4 General Principles 115
4.1 Existence of an LDP and Related Properties 116
4.1.1 Properties of the LDP 117
4.1.2 The Existence of an LDP 120
4.2 Transformations of LDPs 126
4.2.1 Contraction Principles 126
4.2.2 Exponential Approximations 130
4.3 Varadhan s Integral Lemma 137
4.4 Bryc s Inverse Varadhan Lemma 141
4.5 LDP in Topological Vector Spaces 148
4.5.1 A General Upper Bound 149
4.5.2 Convexity Considerations 151
4.5.3 Abstract Gärtner Ellis Theorem 157
4.6 Large Deviations for Projective Limits 161
4.7 The LDP and Weak Convergence in Metric Spaces 168
4.8 Historical Notes and References 173
i
Contents xv
5 Sample Path Large Deviations 175
5.1 Sample Path Large Deviations for Random Walks 176
5.2 Brownian Motion Sample Path Large Deviations 185
5.3 Multivariate Random Walk and Brownian Sheet 188
5.4 Performance Analysis of DMPSK Modulation 193
5.5 Large Exceedances in lRd 200
5.6 The Freidlin Wentzell Theory 212
5.7 The Problem of Diffusion Exit from a Domain 220
5.8 The Performance of Tracking Loops 238
5.8.1 An Angular Tracking Loop Analysis 238
5.8.2 The Analysis of Range Tracking Loops 242
5.9 Historical Notes and References 248
6 The LDP for Abstract Empirical Measures 251
6.1 CrameVs Theorem in Polish Spaces 251
6.2 Sanov s Theorem 260
6.3 LDP for the Empirical Measure—The Uniform Markov
Case 272
6.4 Mixing Conditions and LDP 278
6.4.1 LDP for the Empirical Mean in Htd 279
6.4.2 Empirical Measure LDP for Mixing Processes .... 285
6.5 LDP for Empirical Measures of Markov Chains 289
6.5.1 LDP for Occupation Times 289
6.5.2 LDP for the fc Empirical Measures 295
6.5.3 Process Level LDP for Markov Chains 298
6.6 A Weak Convergence Approach to Large Deviations .... 302
6.7 Historical Notes and References 306
7 Applications of Empirical Measures LDP 311
7.1 Universal Hypothesis Testing 311
7.1.1 A General Statement of Test Optimality 311
7.1.2 Independent and Identically Distributed
Observations 317
7.2 Sampling Without Replacement 318
xvi Contents
7.3 The Gibbs Conditioning Principle 323
7.3.1 The Non Interacting Case 327
7.3.2 The Interacting Case 330
7.3.3 Refinements of the Gibbs Conditioning Principle . . 335
7.4 Historical Notes and References 338
Appendix 341
A Convex Analysis Considerations in TRd 341
B Topological Preliminaries 343
B.l Generalities 343
B.2 Topological Vector Spaces and Weak Topologies . . 346
B.3 Banach and Polish Spaces 347
B.4 Mazur s Theorem 349
C Integration and Function Spaces 350
C.l Additive Set Punctions 350
C.2 Integration and Spaces of Punctions 352
D Probability Measures on Polish Spaces 354
D.l Generalities 354
D.2 Weak Topology 355
D.3 Product Space and Relative Entropy
Decompositions 357
E Stochastic Analysis 359
Bibliography 363
General Conventions 385
Index of Notation 387
Index 391
i
|
| any_adam_object | 1 |
| author | Dembo, Amir Zaitûnî, ʿOfer |
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| author_facet | Dembo, Amir Zaitûnî, ʿOfer |
| author_role | aut aut |
| author_sort | Dembo, Amir |
| author_variant | a d ad ʿ z ʿz |
| building | Verbundindex |
| bvnumber | BV012544787 |
| callnumber-first | Q - Science |
| callnumber-label | QA273 |
| callnumber-raw | QA273.67.D46 1998 |
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| callnumber-subject | QA - Mathematics |
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| ctrlnum | (OCoLC)246687906 (DE-599)BVBBV012544787 |
| dewey-full | 519.5/3421 519.534 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/34 21 519.534 |
| dewey-search | 519.5/34 21 519.534 |
| dewey-sort | 3519.5 234 221 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| isbn | 0387984062 |
| language | German |
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| spelling | Dembo, Amir Verfasser aut Large deviations techniques and applications Amir Dembo ; Ofer Zeitouni 2. ed. New York [u.a.] Springer 1998 XVI, 396 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applications of mathematics 38 Literaturverz. S. 363 - 384 Large deviations Große Abweichung (DE-588)4330658-5 gnd rswk-swf Maximale Abweichung (DE-588)4169156-8 gnd rswk-swf Große Abweichung (DE-588)4330658-5 s DE-604 Maximale Abweichung (DE-588)4169156-8 s Zaitûnî, ʿOfer Verfasser (DE-588)120906058 aut Applications of mathematics 38 (DE-604)BV000895226 38 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008519260&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dembo, Amir Zaitûnî, ʿOfer Large deviations techniques and applications Applications of mathematics Large deviations Große Abweichung (DE-588)4330658-5 gnd Maximale Abweichung (DE-588)4169156-8 gnd |
| subject_GND | (DE-588)4330658-5 (DE-588)4169156-8 |
| title | Large deviations techniques and applications |
| title_auth | Large deviations techniques and applications |
| title_exact_search | Large deviations techniques and applications |
| title_full | Large deviations techniques and applications Amir Dembo ; Ofer Zeitouni |
| title_fullStr | Large deviations techniques and applications Amir Dembo ; Ofer Zeitouni |
| title_full_unstemmed | Large deviations techniques and applications Amir Dembo ; Ofer Zeitouni |
| title_short | Large deviations techniques and applications |
| title_sort | large deviations techniques and applications |
| topic | Large deviations Große Abweichung (DE-588)4330658-5 gnd Maximale Abweichung (DE-588)4169156-8 gnd |
| topic_facet | Large deviations Große Abweichung Maximale Abweichung |
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