A basic course in probability theory:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
2007
|
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 210 S. 235 mm x 155 mm |
| ISBN: | 9780387719382 0387719385 9780387719399 |
Staff View
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Record in the Search Index
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| adam_text | Contents
Preface
vii
I Random Maps, Distribution, and Mathematical Expectation
1
Exercises
................................ 14
II Independence, Conditional Expectation
19
Exercises
................................ 33
III Martingales and Stopping Times
37
Exercises
................................ 47
IV Classical Zero-One Laws, Laws of Large Numbers and Deviations
49
Exercises
................................ 57
V Weak Convergence of Probability Measures
59
Exorcises
................................ 70
VI Fourier Series, Fourier Transform, and Characteristic Functions
73
Exercises
................................ 93
VII
Classical Central Limit Theorems
99
Exercises
................................ 104
VIII
Laplace Transforms and Tauberian Theorem
107
Exorcises
................................ 118
хи
CONTENTS
IX Random Series of Independent Summands
121
Exorcises
.................................
і
27
X Kobnogorov s Extension Theorem and Brownian Motion
129
Exercises
................................ 138
XI Brownian Motion: The
LIL
and Some Fine-Scale Properties
141
Exercises
................................ 145
XII
Skorokhod Embedding and Donsker s
Invariance
Principle
147
Exercises
................................ 164
XIII
A Historical Note on Brownian Motion
167
A Measure and Integration
171
1
Measures and the
Carathéodory
Extension
............. 171
2
Integration and Basic Convergence Theorems
.......... 176
3
Product Measures
.......................... 182
4
Riesz Representation on C(S)
................... 183
В
Topology and Function Spaces
187
С
Hubert Spaces and Applications in Measure Theory
193
1
Hubert spaces
............................. 193
2
Lebesguc Decomposition and
lhe
Radon Nikodym Theorem
. . 196
References
201
Index
205
Symbol Index
211
|
| adam_txt |
Contents
Preface
vii
I Random Maps, Distribution, and Mathematical Expectation
1
Exercises
. 14
II Independence, Conditional Expectation
19
Exercises
. 33
III Martingales and Stopping Times
37
Exercises
. 47
IV Classical Zero-One Laws, Laws of Large Numbers and Deviations
49
Exercises
. 57
V Weak Convergence of Probability Measures
59
Exorcises
. 70
VI Fourier Series, Fourier Transform, and Characteristic Functions
73
Exercises
. 93
VII
Classical Central Limit Theorems
99
Exercises
. 104
VIII
Laplace Transforms and Tauberian Theorem
107
Exorcises
. 118
хи
CONTENTS
IX Random Series of Independent Summands
121
Exorcises
.
і
27
X Kobnogorov's Extension Theorem and Brownian Motion
129
Exercises
. 138
XI Brownian Motion: The
LIL
and Some Fine-Scale Properties
141
Exercises
. 145
XII
Skorokhod Embedding and Donsker's
Invariance
Principle
147
Exercises
. 164
XIII
A Historical Note on Brownian Motion
167
A Measure and Integration
171
1
Measures and the
Carathéodory
Extension
. 171
2
Integration and Basic Convergence Theorems
. 176
3
Product Measures
. 182
4
Riesz Representation on C(S)
. 183
В
Topology and Function Spaces
187
С
Hubert Spaces and Applications in Measure Theory
193
1
Hubert spaces
. 193
2
Lebesguc Decomposition and
lhe
Radon Nikodym Theorem
. . 196
References
201
Index
205
Symbol Index
211 |
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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 |
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| dewey-sort | 3519.2 |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T17:33:18Z |
| indexdate | 2024-07-09T20:57:42Z |
| institution | BVB |
| isbn | 9780387719382 0387719385 9780387719399 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015651016 |
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| owner_facet | DE-355 DE-BY-UBR DE-824 DE-384 DE-11 |
| physical | XII, 210 S. 235 mm x 155 mm |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Springer |
| record_format | marc |
| series2 | Universitext |
| spelling | Bhattacharya, Rabindra N. 1937- Verfasser (DE-588)120600188 aut A basic course in probability theory Rabi Bhattacharya ; Edward C. Waymire New York, NY Springer 2007 XII, 210 S. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Universitext Probabilities Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 s DE-604 Waymire, Edward C. Verfasser (DE-588)130026190 aut Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015651016&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bhattacharya, Rabindra N. 1937- Waymire, Edward C. A basic course in probability theory Probabilities Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| subject_GND | (DE-588)4079013-7 |
| title | A basic course in probability theory |
| title_auth | A basic course in probability theory |
| title_exact_search | A basic course in probability theory |
| title_exact_search_txtP | A basic course in probability theory |
| title_full | A basic course in probability theory Rabi Bhattacharya ; Edward C. Waymire |
| title_fullStr | A basic course in probability theory Rabi Bhattacharya ; Edward C. Waymire |
| title_full_unstemmed | A basic course in probability theory Rabi Bhattacharya ; Edward C. Waymire |
| title_short | A basic course in probability theory |
| title_sort | a basic course in probability theory |
| topic | Probabilities Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| topic_facet | Probabilities Wahrscheinlichkeitstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015651016&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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