A user's guide to measure theoretic probability:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2006
|
| Ausgabe: | Reprinted |
| Schriftenreihe: | Cambridge series in statistical and probabilistic mathematics
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018977790&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XIII, 351 S. graph. Darst. |
| ISBN: | 9780521802420 9780521002899 0521802423 0521002893 |
Internformat
MARC
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| 100 | 1 | |a Pollard, David |d 1950- |e Verfasser |0 (DE-588)110615905 |4 aut | |
| 245 | 1 | 0 | |a A user's guide to measure theoretic probability |c David Pollard |
| 250 | |a Reprinted | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2006 | |
| 300 | |a XIII, 351 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Cambridge series in statistical and probabilistic mathematics | |
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Datensatz im Suchindex
| _version_ | 1819362992131670016 |
|---|---|
| adam_text | Contents
Preface
Chapter
1:
§1
§2
§3
§4
*§5
§6
§7
Chapter
2:
§1
§2
§3
*§4
§5
§6
*§7
*§8
§9
§10
*§11
§12
§13
Chapter
3:
§1
*§2
§3
§4
*§5
*§6
§7
§8
Chapter
4:
§1
§2
§3
§4
*§5
§6
*§7
*§8
xi
Motivation
Why bother with measure theory?
1
The cost and benefit of rigor
3
Where to start: probabilities or expectations?
5
The
de Finetti
notation
7
Fair prices
11
Problems
13
Notes
14
A MODICUM OF MEASURE THEORY
Measures and sigma-fields
17
Measurable functions
22
Integrals
26
Construction of integrals from measures
29
Limit theorems
31
Negligible sets
33
Lp spaces
36
Uniform integrability
37
Image measures and distributions
39
Generating classes of sets
41
Generating classes of functions
43
Problems
45
Notes
51
Densities and derivatives
Densities and absolute continuity
53
The Lebesgue decomposition
58
Distances and affinities between measures
59
The classical concept of absolute continuity
65
Vitali
covering lemma
68
Densities as almost sure derivatives
70
Problems
71
Notes
75
Product spaces and independence
Independence
77
Independence of sigma-fields
80
Construction of measures on a product space
Product measures
88
Beyond sigma-finiteness
93
SLLN via blocking
95
SLLN for identically distributed summands
97
Infinite product spaces
99
83
Contents
§9 Problems 102
§10 Notes 108
Chapter
5:
Conditioning
§1
Conditional distributions: the elementary case 111
§2
Conditional distributions: the general case
113
§3
Integration and disintegration
116
§4
Conditional densities
118
*§5
Invariance
121
§6
Kolmogorov s abstract conditional expectation
123
*§7 Sufficiency
128
§8
Problems
131
§9
Notes
135
Chapter
6:
Martingale et al.
§1
What are they?
138
§2
Stopping times
142
§3
Convergence of positive
supermartingales
147
§4
Convergence of
submartingales
151
*§5 Proof of the Krickeberg decomposition
152
*§6 Uniform integrability
153
*§7 Reversed martingales
155
*§8 Symmetry and exchangeability
159
§9
Problems
162
§10
Notes
166
Chapter
7:
Convergence in distribution
§1
Definition and consequences
169
§2
Lindeberg s method for the central limit theorem
176
§3
Multivariate limit theorems
181
§4
Stochastic order symbols
182
*§5 Weakly convergent subsequences
184
§6
Problems
186
§7
Notes
190
Chapter
8:
Fourier transforms
§1
Definitions and basic properties
193
§2
inversion formula
195
§3
A mystery?
198
§4
Convergence in distribution
198
*§5 A martingale central limit theorem
200
§6
Multivariate Fourier transforms
202
*§7
Cramér-Wold
without Fourier transforms
203
*§8 The
Lévy-Cramér
theorem
205
§9
Problems
206
§10
Notes
208
Contents ix
Chapter
9: Brownian
motion
§1
Prerequisites
211
§2
Brownian motion and Wiener measure
213
§3
Existence of Brownian motion
215
*§4 Finer properties of sample paths
217
§5
Strong Markov property
219
*§6 Martingale characterizations of Brownian motion
222
*§7 Functional of Brownian motion
226
*§8 Option pricing
228
§9
Problems
230
§10
Notes
234
Chapter
10:
Representations and couplings
§1
What is coupling?
237
§2
Almost sure representations
239
*§3 Strassen s Theorem
242
*§4 The Yurinskii coupling
244
§5
Quantile coupling of Binomial with normal
248
§6 Haar
coupling
—
the Hungarian construction
249
§7
The
Komlós-Major-Tusnády
coupling
252
§8
Problems
256
§9
Notes
258
Chapter
11 :
Exponential tails and the law of the iterated logarithm
§1
LIL
for normal summands
261
§2
LIL
for bounded summands
264
*§3 Kolmogorov s exponential lower bound
266
*§4 Identically distributed summands
268
§5
Problems
271
§6
Notes
272
Chapter
12:
Multivariate normal distributions
§1
Introduction
274
*§2 Fernique s inequality
275
*§3 Proof of Fernique s inequality
276
§4
Gaussian isoperimetric inequality
278
*§5 Proof of the isoperimetric inequality
280
§6
Problems
285
§7
Notes
287
Appendix A: Measures and integrals
§1
Measures and inner measure
289
§2
Tightness
291
§3
Countable additivity
292
§4
Extension to the Dc-closure
294
§5
Lebesgue measure
295
§6
Integral representations
296
§7
Problems
300
§8
Notes
300
Contents
Appendix
В:
Hilbert spaces
§1
Definitions
301
§2
Orthogonal projections
302
§3
Orthonormal
bases
303
§4
Series expansions of random processes
305
§5
Problems
306
§6
Notes
306
Appendix C: Convexity
§1
Convex sets and functions
307
§2
One-sided derivatives
308
§3
Integral representations
310
§4
Relative interior of a convex set
312
§5
Separation of convex sets by linear functionals
313
§6
Problems
315
§7
Notes
316
Appendix D: Binomial and normal distributions
§1
Tails of the normal distributions
317
§2
Quantile coupling of Binomial with normal
320
§3
Proof of the approximation theorem
324
§4
Notes
328
Appendix E: Martingales in continuous time
§1
Filtrations, sample paths, and stopping times
329
§2
Preservation of martingale properties at stopping times
332
§3
Supermartingales
from their rational skeletons
334
§4
The Brownian filtration
336
§5
Problems
338
§6
Notes
338
Appendix F: Disintegration of measures
§1
Representation of measures on product spaces
339
§2
Disintegrations with respect to a measurable map
342
§3
Problems
343
§4
Notes
345
Index
347
|
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| discipline | Mathematik Wirtschaftswissenschaften |
| edition | Reprinted |
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| id | DE-604.BV036086846 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T14:06:33Z |
| institution | BVB |
| isbn | 9780521802420 9780521002899 0521802423 0521002893 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018977790 |
| oclc_num | 609902962 |
| open_access_boolean | |
| owner | DE-703 DE-355 DE-BY-UBR |
| owner_facet | DE-703 DE-355 DE-BY-UBR |
| physical | XIII, 351 S. graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series2 | Cambridge series in statistical and probabilistic mathematics |
| spellingShingle | Pollard, David 1950- A user's guide to measure theoretic probability Maßtheorie (DE-588)4074626-4 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| subject_GND | (DE-588)4074626-4 (DE-588)4064324-4 |
| title | A user's guide to measure theoretic probability |
| title_auth | A user's guide to measure theoretic probability |
| title_exact_search | A user's guide to measure theoretic probability |
| title_full | A user's guide to measure theoretic probability David Pollard |
| title_fullStr | A user's guide to measure theoretic probability David Pollard |
| title_full_unstemmed | A user's guide to measure theoretic probability David Pollard |
| title_short | A user's guide to measure theoretic probability |
| title_sort | a user s guide to measure theoretic probability |
| topic | Maßtheorie (DE-588)4074626-4 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| topic_facet | Maßtheorie Wahrscheinlichkeitsrechnung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018977790&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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