Conditional measures and applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | Undetermined |
| Published: |
New York [u.a.]
Dekker
1993
|
| Edition: | 1. print. |
| Series: | Pure and applied mathematics
177 |
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006872676&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Item Description: | Literaturverz. S.398-410 |
| Physical Description: | XIV, 417 S. |
| ISBN: | 0824788842 |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
Preface v
Chapter 1: The Concept of Conditioning 1
1.1 Introduction 1
1.2 Conditonal probability given a partition 3
1.3 Conditional expectation: elementary case 10
1.4 Conditioning with densities 13
1.5 Conditional probability spaces: first steps 18
1.6 Bibliographical notes 23
Chapter 2: The Kolmogorov Formulation and
Its Properties 25
2.1 Introduction of the general concept 25
2.2 Basic properties of conditional expectation 32
2.3 Conditional probabilities in the general case 43
2.4 Remarks on the inclusion of previous concepts 51
2.5 Conditional independence and related concepts 54
2.6 Bibliographical notes 61
xi
xii Contents
Chapter 3: Computational Problems Associated
with Conditioning 63
3.1 Introduction 63
3.2 Some examples with multiple solutions: paradoxes .... 64
3.3 Explanation of paradoxes 75
3.4 Some methods of computation 78
3.5 Remarks on traditional calculations of conditional
measures 84
3.6 Bibliographical notes 88
Chapter 4: An Axiomatic Approach to Conditional
Probability 90
4.1 Introduction 90
4.2 Axiomatization of conditioning based on partitions .... 92
4.3 Structure of the new conditional probability functions . . 96
4.4 Some applications 104
4.5 Difficulties with earlier examples 113
4.6 Bibliographical notes 119
Chapter 5: Regularity of Conditional Measures 122
5.1 Introduction 122
5.2 Existence of regular conditional probabilities:
generalities 123
5.3 Special spaces admitting regular
conditional probabilities 128
5.4 Disintegration of probability measures and
regular conditioning 141
5.5 Further results on disintegration 156
5.6 Evaluation of conditional expectations by Fourier
analysis 161
5.7 Further evaluations of conditional expectations 170
5.8 Bibliographical notes 177
Contents xih
Chapter 6: Sufficiency 180
6.1 Introduction 180
6.2 Conditioning relative to families of measures 184
6.3 Sufficiency: the dominated case 187
6.4 Sufficiency: the undominated case 1%
6.5 Sufficiency: another approach to the undominated case . 208
6.6 Bibliographical notes 214
Chapter 7: Abstraction of Kolmogorov s Formulation 216
7.1 Introduction 216
7.2 Integration relative to conditional measures and
function spaces 218
7.3 Functional characterizations of conditioning 232
7.4 Renyi s formulation as a specialization of the abstract
version 253
7.5 Conditional measures and differentiation 257
7.6 Bibliographical notes 262
Chapter 8: Products of Conditional Measures 264
8.1 Introduction 264
8.2 A general formulation of products 270
8.3 A general projective limit theorem 276
8.4 Some consequences 282
8.5 Remarks on conditioning, disintegration, and lifting . . . 286
8.6 Bibliographical notes 290
Chapter 9: Applications to Martingales and
Markov Processes 292
9.1 Introduction 292
9.2 Set martingales 298
9.3 Martingale convergence 307
9.4 Markov processes: some basic results 317
9.5 Further properties of Markov processes 327
9.6 Bibliographical notes 332
xiv Contents
Chapter 10: Applications to Modern Analysis 334
10.1 Introduction and motivation 334
10.2 Conditional measures and kernels 338
10.3 Reynolds operators and conditional expectations .... 348
10.4 Bistochastic operators and conditioning 350
10.5 Contractive projections and conditional expectations . . 358
10.6 Bibliographical notes 365
Chapter 11: Conditioning in General Structures 368
11.1 Introduction 368
11.2 Averagings in cones of positive functions 370
11.3 Averaging operators on function algebras 373
11.4 Conditioning in operator algebras 376
11.5 Some applications of noncommutative conditioning . . 385
11.6 Bibliographical notes 395
References 398
Notation 411
Index 413
|
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| id | DE-604.BV010326936 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T09:52:05Z |
| institution | BVB |
| isbn | 0824788842 |
| language | Undetermined |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006872676 |
| oclc_num | 246623816 |
| open_access_boolean | |
| owner | DE-20 |
| owner_facet | DE-20 |
| physical | XIV, 417 S. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Dekker |
| record_format | marc |
| series2 | Pure and applied mathematics |
| spellingShingle | Rao, Malempati M. 1929- Conditional measures and applications Wahrscheinlichkeitsmaß swd Bedingte Wahrscheinlichkeitsverteilung (DE-588)4294196-9 gnd Wahrscheinlichkeitsmaß (DE-588)4137556-7 gnd |
| subject_GND | (DE-588)4294196-9 (DE-588)4137556-7 |
| title | Conditional measures and applications |
| title_auth | Conditional measures and applications |
| title_exact_search | Conditional measures and applications |
| title_full | Conditional measures and applications M. M. Rao |
| title_fullStr | Conditional measures and applications M. M. Rao |
| title_full_unstemmed | Conditional measures and applications M. M. Rao |
| title_short | Conditional measures and applications |
| title_sort | conditional measures and applications |
| topic | Wahrscheinlichkeitsmaß swd Bedingte Wahrscheinlichkeitsverteilung (DE-588)4294196-9 gnd Wahrscheinlichkeitsmaß (DE-588)4137556-7 gnd |
| topic_facet | Wahrscheinlichkeitsmaß Bedingte Wahrscheinlichkeitsverteilung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006872676&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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