Convergence of probability measures:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Wiley
1999
|
| Edition: | 2. ed. |
| Series: | Wiley series in probability and statistics : Probability and statistics section
A Wiley interscience publication |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 277 S. |
| ISBN: | 0471197459 9780471197454 |
Staff View
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| 245 | 1 | 0 | |a Convergence of probability measures |c Patrick Billingsley |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Wiley |c 1999 | |
| 300 | |a IX, 277 S. | ||
| 336 | |b txt |2 rdacontent | ||
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Record in the Search Index
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CONTENTS
Introduction l
Chapter 1. Weak Convergence in Metric Spaces 7
Section 1. Measures on Metric Spaces, 7
Measures and Integrals. Tightness. Some Examples. Problems.
Section 2. Properties of Weak Convergence, 14
The Portmanteau Theorem. Other Criteria. The Mapping
Theorem. Product Spaces. Problems.
Section 3. Convergence in Distribution, 24
Random Elements. Convergence in Distribution. Convergence
in Probability. Local vs. Integral Laws. Integration to the Limit.
Relative measure*Three Lemmas* Problems.
Section 4. Long Cycles and Large Divisors,* 38
Long Cycles. The Space A. The Poisson Dirichlet Distribu¬
tion. Size Biased Sampling. Large Prime Divisors. Technical
Arguments. Problems.
Section 5. Prohorov's Theorem, 57
Relative Compactness. Tightness. The Proof. Problems.
Section 6. A Miscellany,* 65
The Ball a Field. Skorohod's Representation Theorem. The
Prohorov Metric. A Coupling Theorem. Problems.
Chapter 2. The Space C 80
Section 7. Weak Convergence and Tightness in C, 80
* Starred topics can be omitted on a first reading
vii
viii Contents
Tightness and Compactness in C. Random Functions. Coordi¬
nate Variables. Problems.
Section 8. Wiener Measure and Donsker's Theorem, 86
Wiener Measure. Construction of Wiener Measure. Donsker's
Theorem. An Application. The Brownian Bridge. Problems.
Section 9. Functions of Brownian Motion Paths, 94
Maximum and Minimum. The Arc Sine Law. The Brownian
Bridge. Problems.
Section 10. Maximal Inequalities,105
Maxima of Partial Sums. A More General Inequality. A Fur¬
ther Inequality. Problems.
Section 11. Trigonometric Series,* 113
Lacunary Series. Incommensurable Arguments. Problem.
Chapter 3. The Space D 121
Section 12. The Geometry of D, 121
The Definition. The Skorohod Topology. Separability and Com¬
pleteness of D. Compactness inD. A Second Characterization
of Compactness. Finite Dimensional Sets. Random Functions
in D. The Poisson Limit* Problems.
Section 13. Weak Convergence and Tightness in D, 138
Finite Dimensional Distributions. Tightness. A Criterion for
Convergence. A Criterion for Existence* Problem.
Section 14. Applications, 146
Donsker's Theorem Again. An Extension. Dominated Mea¬
sures. Empirical Distribution Functions. Random Change of
Time. Renewal Theory. Problems.
Section 15. Uniform Topologies,* 156
The Uniform Metric on D[0,1]. A Theorem of Dudley's. Em¬
pirical Processes Indexed by Convex Sets.
Section 16. The Space £ [0,oo), 166
Definitions. Properties of the Metric. Separability and Com¬
pleteness. Compactness. Finite Dimensional Sets. Weak Con¬
vergence. Tightness. Aldous's Tightness Criterion.
Contents ix
Chapter 4. Dependent Variables 180
Section 17. More on Prime Divisors,* 180
Introduction. A General Limit Theorem. The Brownian Mo¬
tion Limit. The Poisson Process Limit
Section 18. Martingales, 193
Triangular Arrays. Ergodic Martingale Differences
Section 19. Ergodic Processes, 196
The Basic Theorem. Uniform Mixing. Functions of Mixing
Processes. Diophantine Approximation.
Chapter 5. Other Modes of Convergence 207
Section 20. Convergence in Probability, 207
A Convergence in Probability Version of Donsker's Theorem.
Section 21. Approximation by Independent Normal Sequences. 211
Section 22. Strassen's Theorem, 220
The Theorem. Preliminaries on Brownian Motion. Proof of
Strassen's Theorem. Applications.
Appendix M 236
Metric Spaces. Analysis. Convexity. Probability.
Some Notes on the Problems 264
Bibliographical Notes 267
Bibliography 270
Index 275 |
| any_adam_object | 1 |
| author | Billingsley, Patrick 1925-2011 |
| author_GND | (DE-588)171977858 |
| author_facet | Billingsley, Patrick 1925-2011 |
| author_role | aut |
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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 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| series2 | Wiley series in probability and statistics : Probability and statistics section A Wiley interscience publication |
| spelling | Billingsley, Patrick 1925-2011 Verfasser (DE-588)171977858 aut Convergence of probability measures Patrick Billingsley 2. ed. New York [u.a.] Wiley 1999 IX, 277 S. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics : Probability and statistics section A Wiley interscience publication Wahrscheinlichkeitsmaß - Schwache Konvergenz Wahrscheinlichkeitsmaß (DE-588)4137556-7 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Konvergenz (DE-588)4032326-2 gnd rswk-swf Maßtheorie (DE-588)4074626-4 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Wahrscheinlichkeitsmaß (DE-588)4137556-7 s Konvergenz (DE-588)4032326-2 s DE-604 Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s 1\p DE-604 Maßtheorie (DE-588)4074626-4 s 2\p DE-604 Wahrscheinlichkeitstheorie (DE-588)4079013-7 s 3\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008830674&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 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Billingsley, Patrick 1925-2011 Convergence of probability measures Wahrscheinlichkeitsmaß - Schwache Konvergenz Wahrscheinlichkeitsmaß (DE-588)4137556-7 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Konvergenz (DE-588)4032326-2 gnd Maßtheorie (DE-588)4074626-4 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| subject_GND | (DE-588)4137556-7 (DE-588)4079013-7 (DE-588)4032326-2 (DE-588)4074626-4 (DE-588)4064324-4 |
| title | Convergence of probability measures |
| title_auth | Convergence of probability measures |
| title_exact_search | Convergence of probability measures |
| title_full | Convergence of probability measures Patrick Billingsley |
| title_fullStr | Convergence of probability measures Patrick Billingsley |
| title_full_unstemmed | Convergence of probability measures Patrick Billingsley |
| title_short | Convergence of probability measures |
| title_sort | convergence of probability measures |
| topic | Wahrscheinlichkeitsmaß - Schwache Konvergenz Wahrscheinlichkeitsmaß (DE-588)4137556-7 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Konvergenz (DE-588)4032326-2 gnd Maßtheorie (DE-588)4074626-4 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| topic_facet | Wahrscheinlichkeitsmaß - Schwache Konvergenz Wahrscheinlichkeitsmaß Wahrscheinlichkeitstheorie Konvergenz Maßtheorie Wahrscheinlichkeitsrechnung |
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