Large deviations techniques and applications:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Deutsch |
| Veröffentlicht: |
New York [u.a.]
Springer
1998
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Applications of mathematics
38 |
| Schlagwörter: | |
| Links: | 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 |
| Beschreibung: | Literaturverz. S. 363 - 384 |
| Umfang: | XVI, 396 S. graph. Darst. |
| ISBN: | 0387984062 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV012544787 | ||
| 003 | DE-604 | ||
| 005 | 20040406 | ||
| 007 | t| | ||
| 008 | 990427s1998 gw d||| |||| 00||| ger d | ||
| 016 | 7 | |a 956003036 |2 DE-101 | |
| 020 | |a 0387984062 |c Pp. : DM 124.00 |9 0-387-98406-2 | ||
| 035 | |a (OCoLC)246687906 | ||
| 035 | |a (DE-599)BVBBV012544787 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a ger | |
| 044 | |a gw |c DE | ||
| 049 | |a DE-824 |a DE-703 |a DE-29T |a DE-355 |a DE-473 |a DE-384 |a DE-91G |a DE-19 |a DE-521 |a DE-20 |a DE-83 |a DE-11 | ||
| 050 | 0 | |a QA273.67.D46 1998 | |
| 082 | 0 | |a 519.5/34 21 | |
| 082 | 0 | |a 519.534 | |
| 084 | |a SK 800 |0 (DE-625)143256: |2 rvk | ||
| 084 | |a SK 820 |0 (DE-625)143258: |2 rvk | ||
| 084 | |a SK 830 |0 (DE-625)143259: |2 rvk | ||
| 084 | |a MAT 629f |2 stub | ||
| 084 | |a 15 |2 sdnb | ||
| 084 | |a 27 |2 sdnb | ||
| 084 | |a 29 |2 sdnb | ||
| 084 | |a 60F10 |2 msc | ||
| 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. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Applications of mathematics |v 38 | |
| 500 | |a Literaturverz. S. 363 - 384 | ||
| 650 | 4 | |a Large deviations | |
| 650 | 0 | 7 | |a Große Abweichung |0 (DE-588)4330658-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Maximale Abweichung |0 (DE-588)4169156-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Große Abweichung |0 (DE-588)4330658-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Maximale Abweichung |0 (DE-588)4169156-8 |D s |
| 689 | 1 | |5 DE-604 | |
| 700 | 1 | |a Zaitûnî, ʿOfer |e Verfasser |0 (DE-588)120906058 |4 aut | |
| 830 | 0 | |a Applications of mathematics |v 38 |w (DE-604)BV000895226 |9 38 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u 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 |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-008519260 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 629f 2001 A 12361 0102 MAT 629f 2001 A 12362 |
|---|---|
| DE-BY-TUM_katkey | 1461173 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040020249985 040020086331 |
| _version_ | 1821932884122927104 |
| 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 |
| author_GND | (DE-588)120906058 |
| 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 |
| callnumber-search | QA273.67.D46 1998 |
| callnumber-sort | QA 3273.67 D46 41998 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 800 SK 820 SK 830 |
| classification_tum | MAT 629f |
| 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 |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02071nam a2200565 cb4500</leader><controlfield tag="001">BV012544787</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20040406 </controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">990427s1998 gw d||| |||| 00||| ger d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">956003036</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0387984062</subfield><subfield code="c">Pp. : DM 124.00</subfield><subfield code="9">0-387-98406-2</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)246687906</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV012544787</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">ger</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">DE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-824</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-473</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-521</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-11</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA273.67.D46 1998</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519.5/34 21</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519.534</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 800</subfield><subfield code="0">(DE-625)143256:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 820</subfield><subfield code="0">(DE-625)143258:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 830</subfield><subfield code="0">(DE-625)143259:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 629f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">15</subfield><subfield code="2">sdnb</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">27</subfield><subfield code="2">sdnb</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">29</subfield><subfield code="2">sdnb</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">60F10</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Dembo, Amir</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Large deviations techniques and applications</subfield><subfield code="c">Amir Dembo ; Ofer Zeitouni</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">2. ed.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">1998</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVI, 396 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Applications of mathematics</subfield><subfield code="v">38</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Literaturverz. S. 363 - 384</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Large deviations</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Große Abweichung</subfield><subfield code="0">(DE-588)4330658-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Maximale Abweichung</subfield><subfield code="0">(DE-588)4169156-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Große Abweichung</subfield><subfield code="0">(DE-588)4330658-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Maximale Abweichung</subfield><subfield code="0">(DE-588)4169156-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Zaitûnî, ʿOfer</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)120906058</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Applications of mathematics</subfield><subfield code="v">38</subfield><subfield code="w">(DE-604)BV000895226</subfield><subfield code="9">38</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">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</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-008519260</subfield></datafield></record></collection> |
| id | DE-604.BV012544787 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T10:32:12Z |
| institution | BVB |
| isbn | 0387984062 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008519260 |
| oclc_num | 246687906 |
| open_access_boolean | |
| owner | DE-824 DE-703 DE-29T DE-355 DE-BY-UBR DE-473 DE-BY-UBG DE-384 DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-521 DE-20 DE-83 DE-11 |
| owner_facet | DE-824 DE-703 DE-29T DE-355 DE-BY-UBR DE-473 DE-BY-UBG DE-384 DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-521 DE-20 DE-83 DE-11 |
| physical | XVI, 396 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Springer |
| record_format | marc |
| series | Applications of mathematics |
| series2 | Applications of mathematics |
| 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 |
| url | 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 |
| volume_link | (DE-604)BV000895226 |
| work_keys_str_mv | AT demboamir largedeviationstechniquesandapplications AT zaituniʿofer largedeviationstechniquesandapplications |
Inhaltsverzeichnis
Paper/Kapitel scannen lassen
Paper/Kapitel scannen lassen
Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 629f 2001 A 12361 Lageplan 0102 MAT 629f 2001 A 12362 Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |
| Exemplar 2 | Ausleihbar Am Standort |