Probability measures on metric spaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Acad. Press
2005
|
| Edition: | [New ed.] |
| Series: | Probability and mathematical statistics
3 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 276 S. |
| ISBN: | 082183889X |
Staff View
MARC
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| 650 | 4 | |a Metric spaces | |
| 650 | 4 | |a Probability measures | |
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Record in the Search Index
| _version_ | 1804137922361819136 |
|---|---|
| adam_text | CONTENTS
Preface
..............................
v
Chapter I—
The
Borei
Subsets
oí
a Metric Space
1.
General Properties of
Borei
Sets
............... 1
2.
The Isomorphism Theorem
.................. 7
3.
The
Kuratowşki
Theorem
...................
lõ
4.
Borei
Cross Sections in Compact Metric Spaces
......... 22
5.
Borei
Cross Sections in Locally Compact Groups
........ 24
Chapter
11—
Probability Measures in a Metric Space
1.
Regular Measures
...................... 26
2.
Spectrum of a Measure
.................... 27
3.
Tight Measures
....................... 28
4.
Perfect Measures
....................... 30
5.
Linear Functional and Measures
............... 32
6.
The Weak Topology in the Space of Measures
......... 39
7.
Convergence of Sample Distributions
.............. 52
8.
Existence
öf
Nonatomic Measures in Metric Spaces
....... 53
Chapter III—Probability Measures in a Metric Group
1.
The Convolution Operation
..................56
2.
Shift Compactness in
^ã{X)
.................58
3.
Idempotent Measures
.....................61
ix
χ
CONTENTS
4.
Indecomposable Measures
................... 63
5.
The Case When X Is Abelian
................. 70
Chapter IV—Probability Measures in Locally Compact
Abelian Groups
1.
Introduction
......................... 73
2.
Preliminary Facts about a Group and Its Character Group
... 74
3.
Measures and Their Fourier Transforms
............ 74
4.
Infinitely Divisible Distributions
................ 77
5.
General Limit Theorems for Sums of Infinitesimal Summands
. . 82
6.
Gaussian Distributions
.................... 97
7.
Representation of Infinitely Divisible Distributions
....... 102
8.
Uniqueness of the Representation
............... 109
9.
Compactness Criteria
..................... 113
10.
Representation of Convolution Semigroups
........... 116
11.
A Decomposition Theorem
.................. 118
12.
Absolutely Continuous Indecomposable Distributions in X
. . . . 120
Chapter V—The Kolmogorov Consistency Theorem and
Conditional Probability
1.
Statement of the First Problem
................ 131
2.
Standard
Borei
Spaces
.................... 132
3.
The Consistency Theorem in the Case of Inverse Limits of
Borei
Spaces
........................... 137
4.
The Extension Theorem
................... 140
5.
The Kolmogorov Consistency Theorem
............. 143
6.
Statement of the Second Problem
............... 144
7.
Existence of Conditional Probability
.............. 145
8.
Regular Conditional Probability
................ 146
Chapter VI—Probability Measures in a Hilbert Space
1.
Introduction
.........................
loi
2.
Characteristic Functions and Compactness Criteria
....... 151
3.
An Estimate of the Variance
................. 165
4.
Infinitely Divisible Distributions
................ 170
5.
Compactness Criteria
..................... 182
6.
Accompanying Laws
..................... 189
7.
Representation of Convolution Semigroups
........... 201
8.
Decomposition Theorem
.................... 201
9.
Ergodic Theorems
...................... 202
Chapter
VII—
Probability Measures on C[0,
1]
and D[0,
1]
1.
Introduction
......................... 211
2.
Probability Measures on C[0,
1]................ 212
CONTENTS xi
3.
A Condition for the Realization of a Stochastic Process in C
. 215
4.
Convergence to Brownian Motion
............... 219
5.
Distributions of Certain Random Variables Associated with the
Brownian Motion
....................... 224
6.
The Space D[0,
1]...................... 231
7.
Probability Measures in D
................. 249
8.
Ergodic Theorems for -D-Valued Random Variables
....... 254
9.
Applications to Statistical Tests of Hypothesis
......... 259
Bibliographical Notes
........................ 268
Bibliography
............................ 270
List of Symbols
........................... 273
Author Index
............................274
Subject Index
............................275
|
| adam_txt |
CONTENTS
Preface
.
v
Chapter I—
The
Borei
Subsets
oí
a Metric Space
1.
General Properties of
Borei
Sets
. 1
2.
The Isomorphism Theorem
. 7
3.
The
Kuratowşki
Theorem
.
lõ
4.
Borei
Cross Sections in Compact Metric Spaces
. 22
5.
Borei
Cross Sections in Locally Compact Groups
. 24
Chapter
11—
Probability Measures in a Metric Space
1.
Regular Measures
. 26
2.
Spectrum of a Measure
. 27
3.
Tight Measures
. 28
4.
Perfect Measures
. 30
5.
Linear Functional and Measures
. 32
6.
The Weak Topology in the Space of Measures
. 39
7.
Convergence of Sample Distributions
. 52
8.
Existence
öf
Nonatomic Measures in Metric Spaces
. 53
Chapter III—Probability Measures in a Metric Group
1.
The Convolution Operation
.56
2.
Shift Compactness in
^ã{X)
.58
3.
Idempotent Measures
.61
ix
χ
CONTENTS
4.
Indecomposable Measures
. 63
5.
The Case When X Is Abelian
. 70
Chapter IV—Probability Measures in Locally Compact
Abelian Groups
1.
Introduction
. 73
2.
Preliminary Facts about a Group and Its Character Group
. 74
3.
Measures and Their Fourier Transforms
. 74
4.
Infinitely Divisible Distributions
. 77
5.
General Limit Theorems for Sums of Infinitesimal Summands
. . 82
6.
Gaussian Distributions
. 97
7.
Representation of Infinitely Divisible Distributions
. 102
8.
Uniqueness of the Representation
. 109
9.
Compactness Criteria
. 113
10.
Representation of Convolution Semigroups
. 116
11.
A Decomposition Theorem
. 118
12.
Absolutely Continuous Indecomposable Distributions in X
. . . . 120
Chapter V—The Kolmogorov Consistency Theorem and
Conditional Probability
1.
Statement of the First Problem
. 131
2.
Standard
Borei
Spaces
. 132
3.
The Consistency Theorem in the Case of Inverse Limits of
Borei
Spaces
. 137
4.
The Extension Theorem
. 140
5.
The Kolmogorov Consistency Theorem
. 143
6.
Statement of the Second Problem
. 144
7.
Existence of Conditional Probability
. 145
8.
Regular Conditional Probability
. 146
Chapter VI—Probability Measures in a Hilbert Space
1.
Introduction
.
loi
2.
Characteristic Functions and Compactness Criteria
. 151
3.
An Estimate of the Variance
. 165
4.
Infinitely Divisible Distributions
. 170
5.
Compactness Criteria
. 182
6.
Accompanying Laws
. 189
7.
Representation of Convolution Semigroups
. 201
8.
Decomposition Theorem
. 201
9.
Ergodic Theorems
. 202
Chapter
VII—
Probability Measures on C[0,
1]
and D[0,
1]
1.
Introduction
. 211
2.
Probability Measures on C[0,
1]. 212
CONTENTS xi
3.
A Condition for the Realization of a Stochastic Process in "C"
. 215
4.
Convergence to Brownian Motion
. 219
5.
Distributions of Certain Random Variables Associated with the
Brownian Motion
. 224
6.
The Space D[0,
1]. 231
7.
Probability Measures in "D"
. 249
8.
Ergodic Theorems for -D-Valued Random Variables
. 254
9.
Applications to Statistical Tests of Hypothesis
. 259
Bibliographical Notes
. 268
Bibliography
. 270
List of Symbols
. 273
Author Index
.274
Subject Index
.275 |
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| author | Parthasarathy, Kalyanapuram R. 1936- |
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| 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 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | [New ed.] |
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| id | DE-604.BV035004622 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T21:41:39Z |
| indexdate | 2024-07-09T21:19:59Z |
| institution | BVB |
| isbn | 082183889X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016673963 |
| oclc_num | 60791701 |
| open_access_boolean | |
| owner | DE-739 |
| owner_facet | DE-739 |
| physical | XI, 276 S. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Acad. Press |
| record_format | marc |
| series | Probability and mathematical statistics |
| series2 | Probability and mathematical statistics |
| spelling | Parthasarathy, Kalyanapuram R. 1936- Verfasser (DE-588)115641785 aut Probability measures on metric spaces K. R. Parthasarathy [New ed.] New York u.a. Acad. Press 2005 XI, 276 S. txt rdacontent n rdamedia nc rdacarrier Probability and mathematical statistics 3 Espaces métriques Mesures de probabilités Probabilidade larpcal Metric spaces Probability measures Wahrscheinlichkeitsmaß (DE-588)4137556-7 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Maßtheorie (DE-588)4074626-4 gnd rswk-swf Metrischer Raum (DE-588)4169745-5 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s DE-604 Wahrscheinlichkeitsmaß (DE-588)4137556-7 s Metrischer Raum (DE-588)4169745-5 s 1\p DE-604 Maßtheorie (DE-588)4074626-4 s 2\p DE-604 Probability and mathematical statistics 3 (DE-604)BV000892568 3 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016673963&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Parthasarathy, Kalyanapuram R. 1936- Probability measures on metric spaces Probability and mathematical statistics Espaces métriques Mesures de probabilités Probabilidade larpcal Metric spaces Probability measures Wahrscheinlichkeitsmaß (DE-588)4137556-7 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Maßtheorie (DE-588)4074626-4 gnd Metrischer Raum (DE-588)4169745-5 gnd |
| subject_GND | (DE-588)4137556-7 (DE-588)4064324-4 (DE-588)4074626-4 (DE-588)4169745-5 |
| title | Probability measures on metric spaces |
| title_auth | Probability measures on metric spaces |
| title_exact_search | Probability measures on metric spaces |
| title_exact_search_txtP | Probability measures on metric spaces |
| title_full | Probability measures on metric spaces K. R. Parthasarathy |
| title_fullStr | Probability measures on metric spaces K. R. Parthasarathy |
| title_full_unstemmed | Probability measures on metric spaces K. R. Parthasarathy |
| title_short | Probability measures on metric spaces |
| title_sort | probability measures on metric spaces |
| topic | Espaces métriques Mesures de probabilités Probabilidade larpcal Metric spaces Probability measures Wahrscheinlichkeitsmaß (DE-588)4137556-7 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Maßtheorie (DE-588)4074626-4 gnd Metrischer Raum (DE-588)4169745-5 gnd |
| topic_facet | Espaces métriques Mesures de probabilités Probabilidade Metric spaces Probability measures Wahrscheinlichkeitsmaß Wahrscheinlichkeitsrechnung Maßtheorie Metrischer Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016673963&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000892568 |
| work_keys_str_mv | AT parthasarathykalyanapuramr probabilitymeasuresonmetricspaces |