Stochastic convergence of weighted sums of random elements in linear spaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin, [u.a.]
Springer
1978
|
| Series: | Lecture notes in mathematics
672 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VII, 216 Seiten Illustrationen |
| ISBN: | 3540089292 0387089292 |
Staff View
MARC
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| 245 | 1 | 0 | |a Stochastic convergence of weighted sums of random elements in linear spaces |c Robert L. Taylor |
| 264 | 1 | |a Berlin, [u.a.] |b Springer |c 1978 | |
| 300 | |a VII, 216 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 672 | |
| 650 | 4 | |a Espaces vectoriels topologiques | |
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| 650 | 4 | |a Problèmes limites (Théorie des probabilités) | |
| 650 | 4 | |a Processus stochastiques | |
| 650 | 4 | |a Law of large numbers | |
| 650 | 4 | |a Limit theorems (Probability theory) | |
| 650 | 4 | |a Linear topological spaces | |
| 650 | 4 | |a Stochastic processes | |
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Record in the Search Index
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| adam_text |
TABLE OF CONTENTS
GENERAL INTRODUCTION . . 1
I. MATHEMATICAL PRELIMINARIES 6
1.0 Introduction 6
J.1 Linear Spaces and Topologies 6
1.2 Some Basic Mathematical Tools 12
1.3 Basis Theory 14
1.4 Problems 20
II. RANDOM ELEMENTS IN LINEAR SPACES 21
2 .0 Introduction 21
2.1 Definitions and Examples of Random Elements 21
2.2 Topological Properties of Random Elements 25
2.3 Probability Properties of Random Elements 30
2.4 Problems 42
III. LAWS OF LARGE NUMBERS, UNCORRELATION, AND CONVERGENCE OF
WEIGHTED SUMS OF RANDOM VARIABLES 44
3.0 Introduction " . 44
3.1 Laws of Large Numbers for Random Variables 45
3.2 Extensions to Separable Hilbert Spaces 49
3.3 Comparisons of Uncorrelation Concepts 54
3.4 Convergence of Weighted Sums of Random Variables . 63
3.5 Problems 70
IV. LAWS OF LARGE NUMBERS IN NORMED LINEAR SPACES 71
4. 0 Introduction 71
4.1 Laws of Large Numbers for Independent, Identically
Distributed Random Elements 72
4.2 Distributional Conditions and Laws of Large Numbers. . 81
4.3 Beck's Convexity and the Strong Law of Large Numbers . 86
VI
4.4 Other Geometric Conditions and. the Strong
Law of Large Numbers 96
4.5 Other Convergence Results and Extensions to
Frechst Spaces 104
4.6 Problems 106
V. CONVERGENCE OF WEIGHTED SUMS IN NORMED LINEAR SPACES . . 108
5.0 Introduction 108
5.1 Distributional Conditions and Convergence of
Weighted Sums 109
5''. 2 Convergence for Weighted Sums of Tight Random
Elements ¦ 120
5.3 Geometric Conditions and Convergence of Weighted
Sums 137
5.4 Problems 145
VI. RANDOMLY WEIGHTED SUMS 146
6.0 Introduction 146
6.1 Identically Distributed Results 146
6.2 Convergence in the rth Mean for Randomly Weighted
Sums 150
6.3 Problems 152
VII. LAWS OF LARGE NUMBERS IN DC0,1] 153
7.0 Introduction 153
7.1 Preliminaries 154
7.2 Weak laws of Large Numbers in DC0,1] 166
7.3 Strong laws of Large Numbers in DC0,1] 171
7.4 A Discussion of Convex Tightness 179
7.5 Problems 184
VII
VIII. POSSIBLE APPLICATIONS 185
8.0 Introduction 185
Q.I Applications in Stochastic Processes 186
8.2 Applications in Decision Theory 190
8.3 Applications in Quality Control 195
8.4 Applications in Estimation Problems 196
BIBLIOGRAPHY 202
SUBJECT INDEX 212 |
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| discipline | Mathematik |
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| id | DE-604.BV002253149 |
| illustrated | Illustrated |
| indexdate | 2025-02-21T13:01:13Z |
| institution | BVB |
| isbn | 3540089292 0387089292 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001480574 |
| oclc_num | 4194407 |
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| physical | VII, 216 Seiten Illustrationen |
| publishDate | 1978 |
| publishDateSearch | 1978 |
| publishDateSort | 1978 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Taylor, Robert Lewis 1912-1998 (DE-588)1069411558 aut Stochastic convergence of weighted sums of random elements in linear spaces Robert L. Taylor Berlin, [u.a.] Springer 1978 VII, 216 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 672 Espaces vectoriels topologiques Loi des grands nombres Problèmes limites (Théorie des probabilités) Processus stochastiques Law of large numbers Limit theorems (Probability theory) Linear topological spaces Stochastic processes Topologischer Vektorraum (DE-588)4122383-4 gnd rswk-swf Gewichtete Summe (DE-588)4157273-7 gnd rswk-swf Stochastische Konvergenz (DE-588)4183376-4 gnd rswk-swf Stochastische Konvergenz (DE-588)4183376-4 s Gewichtete Summe (DE-588)4157273-7 s DE-604 Topologischer Vektorraum (DE-588)4122383-4 s Erscheint auch als Online-Ausgabe 978-3-540-08929-2 Lecture notes in mathematics 672 (DE-604)BV000676446 672 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001480574&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Taylor, Robert Lewis 1912-1998 Stochastic convergence of weighted sums of random elements in linear spaces Lecture notes in mathematics Espaces vectoriels topologiques Loi des grands nombres Problèmes limites (Théorie des probabilités) Processus stochastiques Law of large numbers Limit theorems (Probability theory) Linear topological spaces Stochastic processes Topologischer Vektorraum (DE-588)4122383-4 gnd Gewichtete Summe (DE-588)4157273-7 gnd Stochastische Konvergenz (DE-588)4183376-4 gnd |
| subject_GND | (DE-588)4122383-4 (DE-588)4157273-7 (DE-588)4183376-4 |
| title | Stochastic convergence of weighted sums of random elements in linear spaces |
| title_auth | Stochastic convergence of weighted sums of random elements in linear spaces |
| title_exact_search | Stochastic convergence of weighted sums of random elements in linear spaces |
| title_full | Stochastic convergence of weighted sums of random elements in linear spaces Robert L. Taylor |
| title_fullStr | Stochastic convergence of weighted sums of random elements in linear spaces Robert L. Taylor |
| title_full_unstemmed | Stochastic convergence of weighted sums of random elements in linear spaces Robert L. Taylor |
| title_short | Stochastic convergence of weighted sums of random elements in linear spaces |
| title_sort | stochastic convergence of weighted sums of random elements in linear spaces |
| topic | Espaces vectoriels topologiques Loi des grands nombres Problèmes limites (Théorie des probabilités) Processus stochastiques Law of large numbers Limit theorems (Probability theory) Linear topological spaces Stochastic processes Topologischer Vektorraum (DE-588)4122383-4 gnd Gewichtete Summe (DE-588)4157273-7 gnd Stochastische Konvergenz (DE-588)4183376-4 gnd |
| topic_facet | Espaces vectoriels topologiques Loi des grands nombres Problèmes limites (Théorie des probabilités) Processus stochastiques Law of large numbers Limit theorems (Probability theory) Linear topological spaces Stochastic processes Topologischer Vektorraum Gewichtete Summe Stochastische Konvergenz |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001480574&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT taylorrobertlewis stochasticconvergenceofweightedsumsofrandomelementsinlinearspaces |