Basic stochastic processes: a course through exercises
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1999
|
| Ausgabe: | 2. print., with corr. |
| Schriftenreihe: | Springer undergraduate mathematics series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 225 S. graph. Darst. |
| ISBN: | 3540761756 |
Internformat
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| 245 | 1 | 0 | |a Basic stochastic processes |b a course through exercises |c Zdzisław Brzézniak and Tomasz Zastawniak |
| 250 | |a 2. print., with corr. | ||
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
1. Review of Probability 1
1.1 Events and Probability 1
1.2 Random Variables 3
1.3 Conditional Probability and Independence 8
1.4 Solutions 10
2. Conditional Expectation 17
2.1 Conditioning on an Event 17
2.2 Conditioning on a Discrete Random Variable 19
2.3 Conditioning on an Arbitrary Random Variable 22
2.4 Conditioning on a cr Field 27
2.5 General Properties 29
2.6 Various Exercises on Conditional Expectation 31
2.7 Solutions 33
3. Martingales in Discrete Time 45
3.1 Sequences of Random Variables 45
3.2 Filtrations 46
3.3 Martingales 48
3.4 Games of Chance 51
3.5 Stopping Times 54
3.6 Optional Stopping Theorem 58
3.7 Solutions 61
4. Martingale Inequalities and Convergence 67
4.1 Doob s Martingale Inequalities 68
ix
x Contents
4.2 Doob s Martingale Convergence Theorem 71
4.3 Uniform Integrability and L1 Convergence of Martingales 73
4.4 Solutions 80
5. Markov Chains 85
5.1 First Examples and Definitions 86
5.2 Classification of States 101
5.3 Long Time Behaviour of Markov Chains: General Case 108
5.4 Long Time Behaviour of Markov Chains with Finite State
Space 114
5.5 Solutions 119
6. Stochastic Processes in Continuous Time 139
6.1 General Notions 139
6.2 Poisson Process 140
6.2.1 Exponential Distribution and Lack of Memory 140
6.2.2 Construction of the Poisson Process 142
6.2.3 Poisson Process Starts from Scratch at Time t 145
6.2.4 Various Exercises on the Poisson Process 148
6.3 Brownian Motion 150
6.3.1 Definition and Basic Properties 151
6.3.2 Increments of Brownian Motion 153
6.3.3 Sample Paths 156
6.3.4 Doob s Maximal 1? Inequality for Brownian Motion .... 159
6.3.5 Various Exercises on Brownian Motion 160
6.4 Solutions 161
7. Ito Stochastic Calculus 179
7.1 Ito Stochastic Integral: Definition 180
7.2 Examples 189
7.3 Properties of the Stochastic Integral 190
7.4 Stochastic Differential and Ito Formula 193
7.5 Stochastic Differential Equations 202
7.6 Solutions 209
Index 223
|
| any_adam_object | 1 |
| author | Brzeźniak, Zdzisław 1958- Zastawniak, Tomasz 1959- |
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| callnumber-first | Q - Science |
| callnumber-label | QA274 |
| callnumber-raw | QA274 |
| callnumber-search | QA274 |
| callnumber-sort | QA 3274 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 820 |
| ctrlnum | (OCoLC)246169050 (DE-599)BVBBV012741886 |
| 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 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. print., with corr. |
| format | Book |
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| indexdate | 2024-07-09T18:32:54Z |
| institution | BVB |
| isbn | 3540761756 |
| language | English |
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| physical | X, 225 S. graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Springer |
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| series2 | Springer undergraduate mathematics series |
| spelling | Brzeźniak, Zdzisław 1958- Verfasser (DE-588)120071193 aut Basic stochastic processes a course through exercises Zdzisław Brzézniak and Tomasz Zastawniak 2. print., with corr. Berlin [u.a.] Springer 1999 X, 225 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer undergraduate mathematics series Stochastischer Prozess - Aufgabensammlung Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Stochastischer Prozess (DE-588)4057630-9 s DE-604 Zastawniak, Tomasz 1959- Verfasser (DE-588)120071231 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008664592&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Brzeźniak, Zdzisław 1958- Zastawniak, Tomasz 1959- Basic stochastic processes a course through exercises Stochastischer Prozess - Aufgabensammlung Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4057630-9 (DE-588)4151278-9 |
| title | Basic stochastic processes a course through exercises |
| title_auth | Basic stochastic processes a course through exercises |
| title_exact_search | Basic stochastic processes a course through exercises |
| title_full | Basic stochastic processes a course through exercises Zdzisław Brzézniak and Tomasz Zastawniak |
| title_fullStr | Basic stochastic processes a course through exercises Zdzisław Brzézniak and Tomasz Zastawniak |
| title_full_unstemmed | Basic stochastic processes a course through exercises Zdzisław Brzézniak and Tomasz Zastawniak |
| title_short | Basic stochastic processes |
| title_sort | basic stochastic processes a course through exercises |
| title_sub | a course through exercises |
| topic | Stochastischer Prozess - Aufgabensammlung Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Stochastischer Prozess - Aufgabensammlung Stochastischer Prozess Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008664592&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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