Essentials of stochastic processes:
Gespeichert in:
1. Verfasser: | |
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Format: | Buch |
Sprache: | English |
Veröffentlicht: |
New York [u.a.]
Springer
2012
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Ausgabe: | 2. ed. |
Schriftenreihe: | Springer Texts in Statistics
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Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | X, 265 S. graph. Darst. |
ISBN: | 9781461436140 |
Internformat
MARC
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245 | 1 | 0 | |a Essentials of stochastic processes |c Richard Durrett |
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Datensatz im Suchindex
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adam_text | Titel: Essentials of stochastic processes
Autor: Durrett, Richard
Jahr: 2012
Contents
1 Markov Chains............................................................... I
1.1 Definitions and Examples............................................. 1
1.2 Multistep Transition Probabilities .................................... 8
1.3 Classification of States ................................................ 12
1.4 Stationary Distributions............................................... 20
1.5 Limit Behavior......................................................... 26
1.6 Special Examples...................................................... 34
1.6.1 Doubly Stochastic Chains..................................... 34
1.6.2 Detailed Balance Condition................................... 37
1.6.3 Reversibility................................................... 42
1.6.4 The Metropolis-Hastings Algorithm ......................... 43
1.7 Proofs of the Main Theorems*........................................ 46
1.8 Exit Distributions...................................................... 52
1.9 Exit Times.............................................................. 58
1.10 Infinite State Spaces*.................................................. 64
1.11 Chapter Summary...................................................... 71
1.12 Exercises............................................................... 75
2 Poisson Processes............................................................. 93
2.1 Exponential Distribution .............................................. 93
2.2 Defining the Poisson Process ......................................... 97
2.3 Compound Poisson Processes......................................... 103
2.4 Transformations........................................................ 106
2.4.1 Thinning....................................................... 106
2.4.2 Superposition.................................................. 107
2.4.3 Conditioning................................................... 108
2.5 Chapter Summary...................................................... 110
2.6 Exercises............................................................... Ill
3 Renewal Processes........................................................... 119
3.1 Laws of Large Numbers............................................... 119
x Contents
3.2 Applications to Queueing Theory..................................... 124
3.2.1 GI/G/1 Queue.................................................. 125
3.2.2 Cost Equations................................................. 126
3.2.3 M/G/l Queue.................................................. 127
3.3 Age and Residual Life* ............................................... 129
3.3.1 DiscreteCase.................................................. 129
3.3.2 General Case................................................... 131
3.4 Chapter Summary...................................................... 133
3.5 Exercises............................................................... 134
4 Continuous Time Markov Chains.......................................... 139
4.1 Definitions and Examples............................................. 139
4.2 Computing the Transition Probability................................ 144
4.3 Limiting Behavior..................................................... 149
4.4 Exit Distributions and Hitting Times................................. 156
4.5 Markovian Queues..................................................... 160
4.6 Queueing Networks*.................................................. 167
4.7 Chapter Summary...................................................... 174
4.8 Exercises............................................................... 175
5 Martingales................................................................... 185
5.1 Conditional Expectation............................................... 185
5.2 Examples, Basic Properties........................................... 188
5.3 Gambling Strategies, Stopping Times................................ 192
5.4 Applications............................................................ 195
5.5 Convergence........................................................... 200
5.6 Exercises............................................................... 204
6 Mathematical Finance....................................................... 209
6.1 Two Simple Examples................................................. 209
6.2 Binomial Model ....................................................... 213
6.3 Concrete Examples.................................................... 218
6.4 Capital Asset Pricing Model .......................................... 223
6.5 American Options..................................................... 226
6.6 Black-Scholes Formula................................................ 230
6.7 Calls and Puts.......................................................... 234
6.8 Exercises............................................................... 236
A Review of Probability........................................................ 241
A. 1 Probabilities, Independence........................................... 241
A.2 Random Variables, Distributions...................................... 245
A.3 Expected Value, Moments............................................. 251
References......................................................................... 259
Index............................................................................... 261
|
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institution | BVB |
isbn | 9781461436140 |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024834548 |
oclc_num | 798916028 |
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physical | X, 265 S. graph. Darst. |
publishDate | 2012 |
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spelling | Durrett, Richard 1951- Verfasser (DE-588)121396789 aut Essentials of stochastic processes Richard Durrett 2. ed. New York [u.a.] Springer 2012 X, 265 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer Texts in Statistics Processos estocásticos larpcal Processus stochastiques Stochastische processen gtt Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4614-3615-7 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024834548&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
spellingShingle | Durrett, Richard 1951- Essentials of stochastic processes Processos estocásticos larpcal Processus stochastiques Stochastische processen gtt Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd |
subject_GND | (DE-588)4057630-9 |
title | Essentials of stochastic processes |
title_auth | Essentials of stochastic processes |
title_exact_search | Essentials of stochastic processes |
title_full | Essentials of stochastic processes Richard Durrett |
title_fullStr | Essentials of stochastic processes Richard Durrett |
title_full_unstemmed | Essentials of stochastic processes Richard Durrett |
title_short | Essentials of stochastic processes |
title_sort | essentials of stochastic processes |
topic | Processos estocásticos larpcal Processus stochastiques Stochastische processen gtt Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd |
topic_facet | Processos estocásticos Processus stochastiques Stochastische processen Stochastic processes Stochastischer Prozess |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024834548&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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