Probability and random processes:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford Univ. Press
2009
|
| Edition: | 3. ed., reprint. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 596 S. |
| ISBN: | 9780198572220 |
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MARC
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Record in the Search Index
| _version_ | 1804143494776750080 |
|---|---|
| adam_text | Contents
1 Events
and their probabilities
1.1
Introduction
1
1.2 Events
as sets
1
1.3
Probability
4
1.4
Conditional probability
8
1.5
Independence
13
1.6
Completeness and product spaces
14
1.7
Worked examples
16
1.8
Problems
21
2
Random variables and their distributions
2.1
Random variables
26
2.2
The law of averages
30
2.3
Discrete and continuous variables
33
2.4
Worked examples
35
2.5
Random vectors
38
2.6
Monte Carlo simulation
41
2.7
Problems
43
3
Discrete random variables
3.1
Probability mass functions
46
3.2
Independence
48
3.3
Expectation
50
3.4
Indicators and matching
56
3.5
Examples of discrete variables
60
3.6
Dependence
62
3.7
Conditional distributions and conditional expectation
67
3.8
Sums of random variables
70
3.9
Simple random walk
71
3.10
Random walk: counting sample paths
75
3.11
Problems
83
Contents
4
Continuous random variables
4.1
Probability density functions
89
4.2
Independence
91
4.3
Expectation
93
4.4
Examples of continuous variables
95
4.5
Dependence
98
4.6
Conditional distributions and conditional expectation
104
4.7
Functions of random variables
107
4.8
Sums of random variables
113
4.9
Multivariate normal distribution
115
4.10
Distributions arising from the normal distribution
119
4.11
Sampling from a distribution
122
4.12
Coupling and
Poisson
approximation
127
4.13
Geometrical probability
133
4.14
Problems
140
5
Generating functions and their applications
5.1
Generating functions
148
5.2
Some applications
156
5.3
Random walk
162
5.4
Branching processes
171
5.5
Age-dependent branching processes
175
5.6
Expectation revisited
178
5.7
Characteristic functions
181
5.8
Examples of characteristic functions
186
5.9
Inversion and continuity theorems
189
5.10
Two limit theorems
193
5.11
Large deviations
201
5.12
Problems
206
6
Markov chains
6.1
Markov processes
213
6.2
Classification of states
220
6.3
Classification of chains
223
6.4
Stationary distributions and the limit theorem
227
6.5
Reversibility
237
6.6
Chains with finitely many states
240
6.7
Branching processes revisited
243
6.8
Birth processes and the
Poisson
process
246
6.9
Continuous-time Markov chains
256
6.10
Uniform semigroups
266
6.11
Birth-death processes and imbedding
268
6.12
Special processes
274
6.13
Spatial
Poisson
processes
281
6.14
Markov chain Monte Carlo
291
6.15
Problems
296
Contents xi
7
Convergence
of random variables
7.1
Introduction
305
7.2
Modes of convergence
308
7.3
Some ancillary results
318
7.4
Laws of large numbers
325
7.5
The strong law
329
7.6
The law of the iterated logarithm
332
7.7
Martingales
333
7.8
Martingale convergence theorem
338
7.9
Prediction and conditional expectation
343
7.10
Uniform integrability
350
7.11
Problems
354
8
Random processes
8.1
Introduction
360
8.2
Stationary processes
361
8.3
Renewal processes
365
8.4
Queues
367
8.5
The Wiener process
370
8.6
Existence of processes
371
8.7
Problems
373
9
Stationary processes
9.1
Introduction
375
9.2
Linear prediction
377
9.3
Autocovariances and spectra
380
9.4
Stochastic integration and the spectral representation
387
9.5
The ergodic theorem
393
9.6
Gaussian processes
405
9.7
Problems
409
10
Renewals
10.1
The renewal equation
412
10.2
Limit theorems
417
10.3
Excess life
421
10.4
Applications
423
10.5
Renewal-reward processes
431
10.6
Problems
437
11
Queues
11.1
Single-server queues
440
11.2
M/M/l
442
11.3
M/G/l
445
11.4
G/M/l
451
11.5
G/G/l
455
xii Contents
11.6
Heavy traffic
462
11.7
Networks of queues
462
11.8
Problems
468
12
Martingales
12.1
Introduction
471
12.2
Martingale differences and Hoeffding s inequality
476
12.3
Crossings and convergence
481
12.4
Stopping times
487
12.5
Optional stopping
491
12.6
The maximal inequality
496
12.7
Backward martingales and continuous-time martingales
499
12.8
Some examples
503
12.9
Problems
508
13
Diffusion processes
13.1
Introduction
513
13.2
Brownian motion
514
13.3
Diffusion processes
516
13.4
First passage times
525
13.5
Barriers
530
13.6
Excursions and the Brownian bridge
534
13.7
Stochastic calculus
537
13.8
The
Ito
integral
539
13.9
Itô s
formula
544
13.10
Option pricing
547
13.11
Passage probabilities and potentials
554
13.12
Problems
561
Appendix I. Foundations and notation
564
Appendix II. Further reading
569
Appendix III. History and varieties of probability
571
Appendix IV. John
Arbuthnoťs
Preface to Of the laws of chance
(1692) 573
Appendix V. Table of distributions
576
Appendix VI. Chronology
578
Bibliography
580
Notation
583
Index
585
|
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| author | Grimmett, Geoffrey 1950- Stirzaker, David |
| author_GND | (DE-588)120872919 |
| author_facet | Grimmett, Geoffrey 1950- Stirzaker, David |
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| building | Verbundindex |
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| classification_tum | MAT 600f |
| ctrlnum | (OCoLC)699647094 (DE-599)BVBBV036802239 |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 3. ed., reprint. |
| format | Book |
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| isbn | 9780198572220 |
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| physical | XII, 596 S. |
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| spelling | Grimmett, Geoffrey 1950- Verfasser (DE-588)120872919 aut Probability and random processes Geoffrey R. Grimmett and David R. Stirzaker 3. ed., reprint. Oxford [u.a.] Oxford Univ. Press 2009 XII, 596 S. txt rdacontent n rdamedia nc rdacarrier Wahrscheinlichkeit (DE-588)4137007-7 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s DE-604 Stochastischer Prozess (DE-588)4057630-9 s 1\p DE-604 Wahrscheinlichkeitstheorie (DE-588)4079013-7 s 2\p DE-604 Wahrscheinlichkeit (DE-588)4137007-7 s 3\p DE-604 Stirzaker, David Verfasser aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020718391&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 | Grimmett, Geoffrey 1950- Stirzaker, David Probability and random processes Wahrscheinlichkeit (DE-588)4137007-7 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| subject_GND | (DE-588)4137007-7 (DE-588)4079013-7 (DE-588)4057630-9 (DE-588)4064324-4 |
| title | Probability and random processes |
| title_auth | Probability and random processes |
| title_exact_search | Probability and random processes |
| title_full | Probability and random processes Geoffrey R. Grimmett and David R. Stirzaker |
| title_fullStr | Probability and random processes Geoffrey R. Grimmett and David R. Stirzaker |
| title_full_unstemmed | Probability and random processes Geoffrey R. Grimmett and David R. Stirzaker |
| title_short | Probability and random processes |
| title_sort | probability and random processes |
| topic | Wahrscheinlichkeit (DE-588)4137007-7 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| topic_facet | Wahrscheinlichkeit Wahrscheinlichkeitstheorie Stochastischer Prozess Wahrscheinlichkeitsrechnung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020718391&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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