Holdings: Basic stochastic processes

Basic stochastic processes: a course through exercises

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Bibliographic Details
Main Authors:	Brzeźniak, Zdzisław 1958- (Author), Zastawniak, Tomasz 1959- (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] Springer 2003
Edition:	6. print.
Series:	Springer undergraduate mathematics series
Subjects:	Stochastischer Prozess Einführung
Online Access:	Inhaltsverzeichnis
Physical Description:	X, 225 S. graph. Darst.
ISBN:	3540761756

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MARC


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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
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spelling	Brzeźniak, Zdzisław 1958- Verfasser (DE-588)120071193 aut Basic stochastic processes a course through exercises Zdzisław Brzézniak and Tomasz Zastawniak 6. print. Berlin [u.a.] Springer 2003 X, 225 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer undergraduate mathematics series 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=010733096&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 (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 (DE-588)4057630-9 gnd
topic_facet	Stochastischer Prozess Einführung
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010733096&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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