Probability: theory and examples
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Belmont, Calif. [u.a.]
Brooks/Cole, Thomson Learning
2005
|
| Ausgabe: | 3. ed. |
| Schriftenreihe: | Duxbury advanced series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 497 S. |
| ISBN: | 0534424414 9780534424411 |
Internformat
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| 100 | 1 | |a Durrett, Richard |d 1951- |e Verfasser |0 (DE-588)121396789 |4 aut | |
| 245 | 1 | 0 | |a Probability |b theory and examples |c Richard Durrett |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a Belmont, Calif. [u.a.] |b Brooks/Cole, Thomson Learning |c 2005 | |
| 300 | |a XI, 497 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Duxbury advanced series | |
| 650 | 7 | |a Probabilités |2 ram | |
| 650 | 7 | |a chaîne Markov |2 inriac | |
| 650 | 7 | |a marche aléatoire |2 inriac | |
| 650 | 7 | |a martingale |2 inriac | |
| 650 | 7 | |a mouvement brownien |2 inriac | |
| 650 | 7 | |a probabilités |2 inriac | |
| 650 | 7 | |a théorie ergodique |2 inriac | |
| 650 | 7 | |a théorie mesure |2 inriac | |
| 650 | 7 | |a théorème limite central |2 inriac | |
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Datensatz im Suchindex
| _version_ | 1804133055464472576 |
|---|---|
| adam_text | Contents
Introductory Lecture
ix
1
Laws of Large Numbers
1
1.
Basic Definitions
1
2.
Random Variables
8
3.
Expected Value
12
a. Inequalities
12
b. Integration to the limit
15
c. Computing expected values
17
4.
Independence
22
a. Sufficient conditions for independence
23
b. Independence, distribution, and expectation
26
с
Constructing independent random variables
31
5.
Weak Laws of Large Numbers
34
a. I? weak laws
34
b. Triangular arrays
37
с
Truncation
40
6.
Borei-Cantelli
Lemmas
46
7.
Strong Law of Large Numbers
55
*8. Convergence of Random Series
60
*9. Large Deviations
69
2
Central Limit Theorems
77
1.
The
De Moivre-Laplace
Theorem
77
2.
Weak Convergence
80
a. Examples
80
b. Theory
83
3.
Characteristic Functions
89
a. Definition, inversion formula
90
b. Weak convergence
97
vi
Contents
с.
Moments
and derivatives
99
*d. Polya s criterion
102
*e. The moment problem
105
4.
Central Limit Theorems
110
a. i.i.d. sequences
110
b. Triangular arrays
114
*c. Prime divisors
(Erdös-Kac) 119
*d. Rates of convergence (Berry-Esseen)
124
*5. Local Limit Theorems
129
6.
Poisson
Convergence
135
a. Basic limit theorem
135
b. Two examples with dependence
140
c. Poisson
processes
143
*7. Stable Laws
147
*8. Infinitely Divisible Distributions
159
*9. Limit theorems in Rd
162
3
Random Walks
171
1.
Stopping Times
171
2.
Recurrence
182
*3. Visits to
0,
Arcsine Laws
195
*4. Renewal Theory
202
4
Martingales
217
1.
Conditional Expectation
217
a. Examples
219
b. Properties
222
*c. Regular conditional probabilities
227
2.
Martingales, Almost Sure Convergence
228
3.
Examples
236
a. Bounded increments
236
b. Polya s urn scheme
238
c. Radon-Nikodym
derivatives
239
d. Branching processes
243
4.
Doob s Inequality, Lp Convergence
246
*
Square
integrable
martingales
252
5.
Uniform Integrability, Convergence in L1
256
6.
Backwards Martingales
262
7.
Optional Stopping Theorems
269
Contents
vii
5
Markov Chains
274
1.
Definitions and Examples
274
2.
Extensions of the Markov Property
282
3.
Recurrence and Transience
288
4.
Stationary Measures
296
5.
Asymptotic Behavior
308
a. Convergence theorems
308
*b. Periodic case
314
*c. Tail
σ
-fìeld
316
*6. General State Space
322
a. Recurrence and transience
325
b. Stationary measures
327
с
Convergence theorem
328
d. GI/G/1 queue
329
6
Ergodic Theorems
332
1.
Definitions and Examples
332
2.
Birkhoff s Ergodic Theorem
337
3.
Recurrence
343
*4. Mixing
347
*5. Entropy
353
*6.
A
Subadditive
Ergodic Theorem
358
*7. Applications
364
7
Brownian Motion
371
1.
Definition and Construction
372
2.
Markov Property, Blumenthal s
0-1
Law
378
3.
Stopping Times, Strong Markov Property
384
4.
Maxima and Zeros
389
5.
Martingales
395
6.
Donsker s Theorem
399
*7. CLT s for Dependent Variables
408
a. Martingales
408
b. Stationary sequences
415
c. Mixing properties
420
*8. Empirical Distributions, Brownian Bridge
425
*9. Laws of the Iterated Logarithm
431
viii Contents
Appendix:
Measure Theory
437
1.
Lebesgue-Stieltjes Measures
437
2.
Carathéodory s
Extension Theorem
444
3.
Completion, etc.
449
4.
Integration
452
5.
Properties of the Integral
461
6.
Product Measures, Fubini s Theorem
466
7.
Kolmogorov s Extension Theorem
471
8.
Radon-Nikodym Theorem
473
9.
Differentiating Under the Integral
478
References
481
Notation
489
Normal Table
492
Index
493
|
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| 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 | 3. ed. |
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| language | English |
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| spelling | Durrett, Richard 1951- Verfasser (DE-588)121396789 aut Probability theory and examples Richard Durrett 3. ed. Belmont, Calif. [u.a.] Brooks/Cole, Thomson Learning 2005 XI, 497 S. txt rdacontent n rdamedia nc rdacarrier Duxbury advanced series Probabilités ram chaîne Markov inriac marche aléatoire inriac martingale inriac mouvement brownien inriac probabilités inriac théorie ergodique inriac théorie mesure inriac théorème limite central inriac Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf 1\p (DE-588)4143389-0 Aufgabensammlung gnd-content Wahrscheinlichkeitstheorie (DE-588)4079013-7 s Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s 2\p DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012999954&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 | Durrett, Richard 1951- Probability theory and examples Probabilités ram chaîne Markov inriac marche aléatoire inriac martingale inriac mouvement brownien inriac probabilités inriac théorie ergodique inriac théorie mesure inriac théorème limite central inriac Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| subject_GND | (DE-588)4079013-7 (DE-588)4064324-4 (DE-588)4143389-0 |
| title | Probability theory and examples |
| title_auth | Probability theory and examples |
| title_exact_search | Probability theory and examples |
| title_full | Probability theory and examples Richard Durrett |
| title_fullStr | Probability theory and examples Richard Durrett |
| title_full_unstemmed | Probability theory and examples Richard Durrett |
| title_short | Probability |
| title_sort | probability theory and examples |
| title_sub | theory and examples |
| topic | Probabilités ram chaîne Markov inriac marche aléatoire inriac martingale inriac mouvement brownien inriac probabilités inriac théorie ergodique inriac théorie mesure inriac théorème limite central inriac Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| topic_facet | Probabilités chaîne Markov marche aléatoire martingale mouvement brownien probabilités théorie ergodique théorie mesure théorème limite central Wahrscheinlichkeitstheorie Wahrscheinlichkeitsrechnung Aufgabensammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012999954&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT durrettrichard probabilitytheoryandexamples |