From uniform laws of large numbers to uniform ergodic theorems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Aarhus
Univ. of Aarhus
2000
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| Series: | Lecture notes series
66 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | V, 142 S. |
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| adam_text | J UNIVERSITY OF AARHUS DEPARTMENT OF MATHEMATICS ISSN: 0065-017X FROM
UNIFORM LAWS OF LARGE NUMBERS TO UNIFORM ERGODIC THEOREMS GORAN PESKIR
2000 B 4839 *TES SERIES NO. 66 DECEPIBER 2000 IE, BLDG. 530
HTTP:ZAVVIW.IMF.AU.DK C, DENMARK INSTITUTIMF.AU.DK CONTENTS 1.
INTRODUCTION 1 1.1 ERGODIC THEOREM 3 1.2 LAW OF LARGE NUMBERS 12 1.3
INFINITE DIMENSIONAL EXTENSIONS 16 1.4 APPLICATIONS TO DYNAMICAL SYSTEMS
19 2. METRIC ENTROPY WITH BRACKETING APPROACH 23 2.1 THE BLUM-DEHARDT
LAW OF LARGE NUMBERS 23 2.2 EXTENSION TO NECESSARY AND SUFFICIENT
CONDITIONS 25 2.3 THE UNIFORM ERGODIC LEMMA 43 2.4 THE UNIFORM ERGODIC
THEOREM FOR DYNAMICAL SYSTEMS 47 2.5 EXAMPLES AND COMPLEMENTS 55 2.5.1
DUDLEY S COUNTER-EXAMPLE 55 2.5.2 NECESSITY OF INTEGRABILITY 56 2.5.3
NECESSITY OF MEASURABILITY 60 2.5.4 GERSTENHABER S COUNTER-EXAMPLE 63
2.5.5 A UNIFORM ERGODIC THEOREM OVER THE ORBIT - WEYL S THEOREM 64 2.5.6
METRIC ENTROPY AND MAJORIZING MEASURE TYPE CONDITIONS 65 3. THE
VAPNIK-CHERVONENKIS APPROACH 71 3.1 THE SUBGAUSSIAN INEQUALITY FOR
RADEMACHER SERIES 71 3.2 SLEPIAN S LEMMA AND SUDAKOV S MINORATION 72 3.3
RADEMACHER AND GAUSSIAN RANDOMIZATION 76 3.4 THE VC LAW OF LARGE NUMBERS
81 3.5 THE VC CLASSES OF SETS 85 3.6 THE EBERLEIN LEMMA 87 3.7 THE
UNIFORM ERGODIC THEOREM FOR ABSOLUTELY REGULAR DYNAMICAL SYSTEMS 89 3.8
EXTENSION TO SEMI-FLOWS AND (NON-LINEAR) OPERATORS 98 3.9 UNIFORMITY
OVER FACTORIZATIONS 103 3.10 EXAMPLES AND COMPLEMENTS 106 3.10.1
EXAMPLES OF VC CLASSES OF SETS 106 3.10.2 WEBER S COUNTER-EXAMPLE 107
3.10.3 TALAGRAND S CONDITION AND NOBEL S COUNTER-EXAMPLE 109 3.10.4
UNIFORM CONVERGENCE OF MOVING AVERAGES ILL 3.10.5 METRIC ENTROPY AND
MAJORIZING MEASURE TYPE CONDITIONS 112 4. THE SPECTRAL REPRESENTATION
THEOREM APPROACH 114 4.1 THE PROBLEM OF UNIFORM CONVERGENCE IN THE WIDE
SENSE STATIONARY CASE 114 4.2 THE UNIFORM MEAN-SQUARE ERGODIC THEOREM
(THE DISCRETE PARAMETER CASE) 115 4.3 THE UNIFORM MEAN-SQUARE ERGODIC
THEOREM (THE CONTINUOUS PARAMETER CASE) 124 4.4 UNIFORM CONVERGENCE OF
ALMOST PERIODIC SEQUENCES 129 SUPPLEMENT: HARDY S REGULAR CONVERGENCE,
UNIFORM CONVERGENCE OF REVERSED MARTINGALES, AND CONSISTENCY OF
STATISTICAL MODELS 132 REFERENCES 138
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| spelling | Peskir, Goran Verfasser (DE-588)13209116X aut From uniform laws of large numbers to uniform ergodic theorems Goran Peskir Aarhus Univ. of Aarhus 2000 V, 142 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes series 66 Ergodensatz (DE-588)4152756-2 gnd rswk-swf Gesetz der großen Zahlen (DE-588)4157077-7 gnd rswk-swf Gesetz der großen Zahlen (DE-588)4157077-7 s Ergodensatz (DE-588)4152756-2 s DE-604 Lecture notes series 66 (DE-604)BV012615812 66 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009298057&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Peskir, Goran From uniform laws of large numbers to uniform ergodic theorems Lecture notes series Ergodensatz (DE-588)4152756-2 gnd Gesetz der großen Zahlen (DE-588)4157077-7 gnd |
| subject_GND | (DE-588)4152756-2 (DE-588)4157077-7 |
| title | From uniform laws of large numbers to uniform ergodic theorems |
| title_auth | From uniform laws of large numbers to uniform ergodic theorems |
| title_exact_search | From uniform laws of large numbers to uniform ergodic theorems |
| title_full | From uniform laws of large numbers to uniform ergodic theorems Goran Peskir |
| title_fullStr | From uniform laws of large numbers to uniform ergodic theorems Goran Peskir |
| title_full_unstemmed | From uniform laws of large numbers to uniform ergodic theorems Goran Peskir |
| title_short | From uniform laws of large numbers to uniform ergodic theorems |
| title_sort | from uniform laws of large numbers to uniform ergodic theorems |
| topic | Ergodensatz (DE-588)4152756-2 gnd Gesetz der großen Zahlen (DE-588)4157077-7 gnd |
| topic_facet | Ergodensatz Gesetz der großen Zahlen |
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| work_keys_str_mv | AT peskirgoran fromuniformlawsoflargenumberstouniformergodictheorems |