Basic stochastic processes: a course through exercises
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2002
|
| Ausgabe: | 4. print. |
| Schriftenreihe: | Springer undergraduate mathematics series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 225 S. graph. Darst. |
| ISBN: | 3540761756 |
Internformat
MARC
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| 245 | 1 | 0 | |a Basic stochastic processes |b a course through exercises |c Zdzisław Brzézniak and Tomasz Zastawniak |
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| 490 | 0 | |a Springer undergraduate mathematics series | |
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Datensatz im Suchindex
| _version_ | 1804129253506154496 |
|---|---|
| adam_text | IMAGE 1
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
IMAGE 2
CONTENTS
; 4.2 DOOB S MARTINGALE CONVERGENCE THEOREM 71
4.3 UNIFORM INTEGRABILITY AND L 1 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 L 2 INEQUALITY FOR BROWNIAN MOTION 159 6.3.5
VARIOUS EXERCISES ON BROWNIAN MOTION . 160
6.4 SOLUTIONS 161
7. LTD 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- |
| author_GND | (DE-588)120071193 (DE-588)120071231 |
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| classification_rvk | QH 237 SK 820 |
| classification_tum | MAT 605f |
| ctrlnum | (OCoLC)248783465 (DE-599)BVBBV014374143 |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 4. print. |
| format | Book |
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| genre | 1\p (DE-588)4151278-9 Einführung gnd-content |
| genre_facet | Einführung |
| id | DE-604.BV014374143 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:02:12Z |
| institution | BVB |
| isbn | 3540761756 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009846652 |
| oclc_num | 248783465 |
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| owner_facet | DE-91G DE-BY-TUM DE-945 DE-11 DE-188 |
| physical | X, 225 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Springer |
| record_format | marc |
| 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 4. print. Berlin [u.a.] Springer 2002 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 1\p (DE-588)4151278-9 Einführung gnd-content Stochastischer Prozess (DE-588)4057630-9 s DE-604 Zastawniak, Tomasz 1959- Verfasser (DE-588)120071231 aut SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009846652&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| 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=009846652&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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