Stochastic convergence:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Academic Press
1975
|
| Ausgabe: | Second edition, |
| Schriftenreihe: | Probability and mathematical statistics
Volume 30 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xi, 200 Seiten Illustrationen |
| ISBN: | 0124598609 |
Internformat
MARC
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| 245 | 1 | 0 | |a Stochastic convergence |c Eugene Lukacs |
| 250 | |a Second edition, | ||
| 264 | 1 | |a New York [u.a.] |b Academic Press |c 1975 | |
| 300 | |a xi, 200 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Probability and mathematical statistics |v Volume 30 | |
| 650 | 4 | |a Convergence (Mathématiques) | |
| 650 | 4 | |a Processus stochastiques | |
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Datensatz im Suchindex
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| adam_text |
CONTENTS
Preface to the Second Edition vii
Preface to the First Edition ix
List of Examples xi
Chapter I. INTRODUCTION 1
1.1. Survey of basic concepts 1
1.2. Certain inequalities 6
1.3. Characteristic functions 13
1.4. Independence 19
1.5. Monotone classes of sets (events) 23
Exercises 25
Chapter II. STOCHASTIC CONVERGENCE CONCEPTS
AND THEIR PROPERTIES 27
2.1. Definitions 27
2.2. Relations among the various convergence concepts 33
2.3. Convergence of sequences of mean values and of certain functions
of random variables 40
2.4. Criteria for stochastic convergence 44
2.5. Further modes of stochastic convergence 50
2.6. Information convergence 54
Exercises 57
Chapter III. SPACES OF RANDOM VARIABLES 60
3.1. Convergence in probability 61
3.2. Almost certain convergence 68
3.3. The spaces Lp 68
3.4. The space of distribution functions 70
Exercises 74
Chapter IV. INFINITE SERIES OF RANDOM VARIABLES
AND RELATED TOPICS 76
4.1. The lemmas of Borel-Cantelli and the zero-one laws 76
4.2. Convergence of series 80
4.3. Some limit theorems 94
Exercises 110
v
vi Contents
Chapter V. RANDOM POWER SERIES 112
5.1. Definition and convergence of random power series 112
5.2. The radius of convergence of a random power series 117
5.3. Random power series with identically distributed coefficients 122
5.4. Random power series with independent coefficients 127
5.5. The analytic continuation of random power series 130
5.6. Random entire functions 135
Exercises 141
Chapter VI. STOCHASTIC INTEGRALS AND DERIVATIVES 143
6.1. Some definitions concerning stochastic processes 143
6.2. Definition and existence of stochastic integrals 145
6.3. L2-continuity and differentiation of stochastic processes 152
Exercises 154
Chapter VII. CHARACTERIZATION OF THE NORMAL
DISTRIBUTION BY PROPERTIES OF INFINITE
SUMS OF RANDOM VARIABLES 157
7.1. Identically distributed linear forms 157
7.2. A linear form and a monomial having the same distribution 161
7.3. Independently distributed infinite sums 168
Exercises 170
Chapter VIII. CHARACTERIZATION OF SOME STOCHASTIC
PROCESSES 172
8.1. Independence and a regression property of two stochastic
integrals 172
8.2. Identically distributed stochastic integrals 175
8.3. Identity of the distribution of a stochastic integral and the
increment of a process 178
8.4. Characterization of stable processes 182
Exercises 189
References 191
Index 195 |
| any_adam_object | 1 |
| author | Lukacs, Eugene 1906-1987 |
| author_GND | (DE-588)128913770 |
| author_facet | Lukacs, Eugene 1906-1987 |
| author_role | aut |
| author_sort | Lukacs, Eugene 1906-1987 |
| author_variant | e l el |
| building | Verbundindex |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 170 SK 820 SK 800 |
| ctrlnum | (OCoLC)1504668 (DE-599)BVBBV001963113 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | Second edition, |
| format | Book |
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| id | DE-604.BV001963113 |
| illustrated | Illustrated |
| indexdate | 2024-09-23T18:07:07Z |
| institution | BVB |
| isbn | 0124598609 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001280246 |
| oclc_num | 1504668 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-473 DE-BY-UBG DE-703 DE-739 DE-355 DE-BY-UBR DE-29T DE-19 DE-BY-UBM DE-384 DE-83 DE-706 DE-188 |
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| physical | xi, 200 Seiten Illustrationen |
| publishDate | 1975 |
| publishDateSearch | 1975 |
| publishDateSort | 1975 |
| publisher | Academic Press |
| record_format | marc |
| series | Probability and mathematical statistics |
| series2 | Probability and mathematical statistics |
| spelling | Lukacs, Eugene 1906-1987 (DE-588)128913770 aut Stochastic convergence Eugene Lukacs Second edition, New York [u.a.] Academic Press 1975 xi, 200 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Probability and mathematical statistics Volume 30 Convergence (Mathématiques) Processus stochastiques Suites (Mathématiques) Convergence Sequences (Mathematics) Stochastic processes Stochastik (DE-588)4121729-9 gnd rswk-swf Stochastische Konvergenz (DE-588)4183376-4 gnd rswk-swf Konvergenz (DE-588)4032326-2 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Zufällige Folge (DE-588)4191092-8 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Konvergenz (DE-588)4032326-2 s Stochastischer Prozess (DE-588)4057630-9 s DE-604 Zufällige Folge (DE-588)4191092-8 s Stochastische Konvergenz (DE-588)4183376-4 s Stochastik (DE-588)4121729-9 s Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s Erscheint auch als Online-Ausgabe 978-0-12-459860-7 Probability and mathematical statistics Volume 30 (DE-604)BV000892568 30 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001280246&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lukacs, Eugene 1906-1987 Stochastic convergence Probability and mathematical statistics Convergence (Mathématiques) Processus stochastiques Suites (Mathématiques) Convergence Sequences (Mathematics) Stochastic processes Stochastik (DE-588)4121729-9 gnd Stochastische Konvergenz (DE-588)4183376-4 gnd Konvergenz (DE-588)4032326-2 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Zufällige Folge (DE-588)4191092-8 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4121729-9 (DE-588)4183376-4 (DE-588)4032326-2 (DE-588)4064324-4 (DE-588)4191092-8 (DE-588)4057630-9 |
| title | Stochastic convergence |
| title_auth | Stochastic convergence |
| title_exact_search | Stochastic convergence |
| title_full | Stochastic convergence Eugene Lukacs |
| title_fullStr | Stochastic convergence Eugene Lukacs |
| title_full_unstemmed | Stochastic convergence Eugene Lukacs |
| title_short | Stochastic convergence |
| title_sort | stochastic convergence |
| topic | Convergence (Mathématiques) Processus stochastiques Suites (Mathématiques) Convergence Sequences (Mathematics) Stochastic processes Stochastik (DE-588)4121729-9 gnd Stochastische Konvergenz (DE-588)4183376-4 gnd Konvergenz (DE-588)4032326-2 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Zufällige Folge (DE-588)4191092-8 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Convergence (Mathématiques) Processus stochastiques Suites (Mathématiques) Convergence Sequences (Mathematics) Stochastic processes Stochastik Stochastische Konvergenz Konvergenz Wahrscheinlichkeitsrechnung Zufällige Folge Stochastischer Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001280246&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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