Large deviations techniques and applications:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg
Springer
2010
|
| Edition: | corrected printing of the 1998 Edition |
| Series: | Stochastic modelling and applied probability
38 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 363 - 384 |
| Physical Description: | xvi, 396 Seiten Diagramme |
| ISBN: | 9783642033100 |
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MARC
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| 245 | 1 | 0 | |a Large deviations techniques and applications |c Amir Dembo; Ofer Zeitouni |
| 250 | |a corrected printing of the 1998 Edition | ||
| 264 | 1 | |a Berlin ; Heidelberg |b Springer |c 2010 | |
| 300 | |a xvi, 396 Seiten |b Diagramme | ||
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| 490 | 1 | |a Stochastic modelling and applied probability |v 38 | |
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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
Cramer s Theorem for Finite Alphabets in
IR
..... 18
2.1.3
Large Deviations for Sampling Without Replacement
. 20
2.2
Cramer s Theorem
........................ 26
2.2.1
Cramer s Theorem in
H
................. 26
2.2.2
Cramer s Theorem in Ed
................ 36
2.3
The Gartner-Ellis Theorem
................... 43
2.4
Concentration Inequalities
.................... 55
2.4.1
Inequalities for Bounded
Martingale
Differences
.... 55
2.4.2
Talagrand s Concentration Inequalities
......... 60
2.5
Historical Notes and References
................. 68
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 Functional 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
IR
......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
5NTENTS 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
IR**
....................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
Cramer s 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
ÌRd
...........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 ¿-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 Optimally
.......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 IRrf
.............341
В
Topological Preliminaries
....................343
B.I Generalities
........................343
B.2 Topological Vector Spaces and Weak Topologies
. . . 346
B.3 Banach and Polish Spaces
................347
B.4 Mazur s Theorem
.....................349
С
Integration and Function Spaces
................350
C.I Additive Set Functions
..................350
C.2 Integration and Spaces of Functions
..........352
D
Probability Measures on Polish Spaces
.............354
D.I 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
Glossary
387
Index
391
|
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| discipline | Mathematik |
| edition | corrected printing of the 1998 Edition |
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| indexdate | 2024-07-09T22:37:15Z |
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| language | English |
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| series | Stochastic modelling and applied probability |
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| spelling | Dembo, Amir 1958- (DE-588)1243438290 aut Large deviations techniques and applications Amir Dembo; Ofer Zeitouni corrected printing of the 1998 Edition Berlin ; Heidelberg Springer 2010 xvi, 396 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Stochastic modelling and applied probability 38 Literaturverz. S. 363 - 384 Maximale Abweichung (DE-588)4169156-8 gnd rswk-swf Große Abweichung (DE-588)4330658-5 gnd rswk-swf Große Abweichung (DE-588)4330658-5 s DE-604 Maximale Abweichung (DE-588)4169156-8 s Zaitûnî, ʿOfer (DE-588)120906058 aut Erscheint auch als Online-Ausgabe 978-3-642-03311-7 Stochastic modelling and applied probability 38 (DE-604)BV019623501 38 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020195531&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dembo, Amir 1958- Zaitûnî, ʿOfer Large deviations techniques and applications Stochastic modelling and applied probability Maximale Abweichung (DE-588)4169156-8 gnd Große Abweichung (DE-588)4330658-5 gnd |
| subject_GND | (DE-588)4169156-8 (DE-588)4330658-5 |
| 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 | Maximale Abweichung (DE-588)4169156-8 gnd Große Abweichung (DE-588)4330658-5 gnd |
| topic_facet | Maximale Abweichung Große Abweichung |
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