Holdings: Martingales and stochastic analysis

Martingales and stochastic analysis:

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Bibliographic Details
Main Author:	Yeh, James (Author)
Format:	Book
Language:	English
Published:	Singapore [u.a.] World Scientific 1995
Series:	Series on multivariate analysis 1
Subjects:	Analyse stochastique Martingales (mathématiques) Martingales (Mathematics) Stochastic analysis Stochastische Analysis Martingal Stochastischer Prozess
Online Access:	Inhaltsverzeichnis
Physical Description:	XIII, 501 S.
ISBN:	981022477X

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MARC


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Record in the Search Index

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adam_text	SERIES ON .J MA RTINGALES AND STOCHASTIC ANALYSIS J. YEH DEPARTMENT OF MATHEMATICS UNIVERSITY 0/ CALIFORNIA, IRVINE WORLD SCIENTIFIC SINGAPORE * NEW JERSEY * LONDON * HONG KONG CONTENTS PREFACE V NOTATIONS XI 1 STOCHASTIC PROCESSES 1 §1 GENERATED A -ALGEBRAS 1 §2 STOCHASTIC PROCESSES 11 [I] MEASURABLE AND PROGRESSIVELY MEASURABLE PROCESSES 11 [II] PREDICTABLE PROCESSES 19 §3 STOPPING TIMES 25 [I] STOPPING TIMES FOR STOCHASTIC PROCESSES WITH CONTINUOUS TIME . . . . 25 [II] STOPPING TIMES FOR STOCHASTIC PROCESSES WITH DISCRETE TIME 39 [III] RANDOM VARIABLES AT STOPPING TIMES 41 [IV] STOPPED PROCESSES AND TRUNCATED PROCESSES 45 §4 CONVERGENCE IN L P AND UNIFORM INTEGRABILITY 49 [I] CONVERGENCE IN L P 49 [II] UNIFORMLY INTEGRABLE SYSTEMS OF RANDOM VARIABLES 53 2 MARTINGALES 71 §5 MARTINGALE, SUBMARTINGALE AND SUPERMARTINGALE 71 [I] MARTINGALE, SUBMARTINGALE AND SUPERMARTINGALE PROPERTIES 71 [II] CONVEXITY THEOREMS 76 [IIIJ DISCRETE TIME INCREASING PROCESSES AND DOOB DECOMPOSITION . . . . 78 [IV] MARTINGALE TRANSFORM 81 [V] SOME EXAMPLES 84 §6 FUNDAMENTAL SUBMARTINGALE INEQUALITIES 86 [I] OPTIONAL STOPPING AND OPTIONAL SAMPLING 87 [II] MAXIMAL AND MINIMAL INEQUALITIES 93 [III] UPCROSSING AND DOWNCROSSING INEQUALITIES 101 VN VIII CONTENTS §7 CONVERGENCE OF SUBMARTINGALES 110 [I] CONVERGENCE OF SUBMARTINGALES WITH DISCRETE TIME 110 [II] CONVERGENCE OF SUBMARTINGALES WITH CONTINUOUS TIME 114 [III] CLOSING A SUBMARTINGALE WITH A FINAL ELEMENT 116 [IV] DISCRETE TIME 1,2-MARTINGALES 119 §8 UNIFORMLY INTEGRABLE SUBMARTINGALES 122 [I] CONVERGENCE OF UNIFORMLY INTEGRABLE SUBMARTINGALES 122 [II] SUBMARTINGALES WITH REVERSED TIME 124 [HI] OPTIONAL SAMPLING BY UNBOUNDED STOPPING TIMES 131 [IV] UNIFORM INTEGRABILITY OF RANDOM VARIABLES AT STOPPING TIMES . . . . 141 §9 REGULARITY OF SAMPLE FUNCTIONS OF SUBMARTINGALES 145 [I] SAMPLE FUNCTIONS OF RIGHT-CONTINUOUS SUBMARTINGALES 145 [II] RIGHT-CONTINUOUS MODIFICATION OF A SUBMARTINGALE 149 §10 INCREASING PROCESSES 155 [I] THE LEBESGUE STIELTJES INTEGRAL 155 [II] INTEGRATION WITH RESPECT TO INCREASING PROCESSES 158 [III] DOOB-MEYER DECOMPOSITION 171 [IV] REGULAR SUBMARTINGALES 187 3 STOCHASTIC INTEGRALS 197 §11 L2-MARTINGALES AND QUADRATIC VARIATION PROCESSES 197 [I] THE SPACE OF RIGHT-CONTINUOUS ^-MARTINGALES 197 [II] SIGNED LEBESGUE-STIELTJES MEASURES 205 [III] LOCALLY BOUNDED VARIATION PROCESSES 207 [IV] QUADRATIC VARIATION PROCESSES 212 §12 STOCHASTIC INTEGRALS WITH RESPECT TO MARTINGALES , 221 [I] STOCHASTIC INTEGRAL OF BOUNDED LEFT-CONTINUOUS ADAPTED SIMPLE PROCESSES W. R. T. L 2 -MARTINGALES 222 [II] STOCHASTIC INTEGRAL OF PREDICTABLE PROCESSES W. R. T. I^-MARTINGALES . . 235 §13 ADAPTED BROWNIAN MOTIONS 262 [I] PROCESSES WITH INDEPENDENT INCREMENTS 262 [II] BROWNIAN MOTIONS IN R D 270 [III] 1-DIMENSIONAL BROWNIAN MOTIONS 286 [IV] STOCHASTIC INTEGRALS WITH RESPECT TO A BROWNIAN MOTION 290 §14 EXTENSIONS OF THE STOCHASTIC INTEGRAL 297 [I] LOCAL I^-MARTINGALES AND THEIR QUADRATIC VARIATION PROCESSES 297 [II] EXTENSIONS OF THE STOCHASTIC INTEGRAL TO LOCAL MARTINGALES 306 CONTENTS IX §15 ITO S FORMULA 318 [I] CONTINUOUS LOCAL SEMIMARTINGALES AND ITO S FORMULA 318 [II] STOCHASTIC INTEGRALS WITH RESPECT TO QUASIMARTIGALES 333 [III] EXPONENTIAL QUASIMARTINGALES 335 [IV] MULTIDIMENSIONAL ITO S FORMULA 340 §16 ITO S STOCHASTIC CALCULUS 344 [I] THE SPACE OF STOCHASTIC DIFFERENTIALS 344 [II] FISK-STRATONOVICH INTEGRALS 352 4 STOCHASTIC DIFFERENTIAL EQUATIONS 357 §17 THE SPACE OF CONTINUOUS FUNCTIONS 357 [I] FUNCTION SPACE REPRESENTATION OF CONTINUOUS PROCESSES 357 [II] METRIZATION OF THE SPACE OF CONTINUOUS FUNCTIONS 364 §18 DEFINITION AND FUNCTION SPACE REPRESENTATION OF SOLUTION 368 [I] DEFINITION OF SOLUTIONS 368 [II] FUNCTION SPACE REPRESENTATION OF SOLUTIONS 372 [III] INITIAL VALUE PROBLEMS 385 §19 EXISTENCE AND UNIQUENESS OF SOLUTIONS 395 [I] UNIQUENESS IN PROBABILITY LAW AND PATHWISE UNIQUENESS OF SOLUTIONS . 395 [II] SIMULTANEOUS REPRESENTATION OF TWO SOLUTIONS ON A FUNCTION SPACE . . 405 §20 STRONG SOLUTIONS 419 [I] EXISTENCE OF STRONG SOLUTIONS 419 [II] UNIQUENESS OF STRONG SOLUTIONS 432 A STOCHASTIC INDEPENDENCE 443 B CONDITIONAL EXPECTATIONS 453 C REGULAR CONDITIONAL PROBABILITIES 475 D MULTIDIMENSIONAL NORMAL DISTRIBUTIONS 487 BIBLIOGRAPHY 495 INDEX * 498
any_adam_object	1
author	Yeh, James
author_facet	Yeh, James
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discipline	Mathematik
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spelling	Yeh, James Verfasser aut Martingales and stochastic analysis J. Yeh Singapore [u.a.] World Scientific 1995 XIII, 501 S. txt rdacontent n rdamedia nc rdacarrier Series on multivariate analysis 1 Analyse stochastique ram Martingales (mathématiques) ram Martingales (Mathematics) Stochastic analysis Stochastische Analysis (DE-588)4132272-1 gnd rswk-swf Martingal (DE-588)4126466-6 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Martingal (DE-588)4126466-6 s DE-604 Stochastischer Prozess (DE-588)4057630-9 s Stochastische Analysis (DE-588)4132272-1 s Series on multivariate analysis 1 (DE-604)BV010950028 1 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007323888&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Yeh, James Martingales and stochastic analysis Series on multivariate analysis Analyse stochastique ram Martingales (mathématiques) ram Martingales (Mathematics) Stochastic analysis Stochastische Analysis (DE-588)4132272-1 gnd Martingal (DE-588)4126466-6 gnd Stochastischer Prozess (DE-588)4057630-9 gnd
subject_GND	(DE-588)4132272-1 (DE-588)4126466-6 (DE-588)4057630-9
title	Martingales and stochastic analysis
title_auth	Martingales and stochastic analysis
title_exact_search	Martingales and stochastic analysis
title_full	Martingales and stochastic analysis J. Yeh
title_fullStr	Martingales and stochastic analysis J. Yeh
title_full_unstemmed	Martingales and stochastic analysis J. Yeh
title_short	Martingales and stochastic analysis
title_sort	martingales and stochastic analysis
topic	Analyse stochastique ram Martingales (mathématiques) ram Martingales (Mathematics) Stochastic analysis Stochastische Analysis (DE-588)4132272-1 gnd Martingal (DE-588)4126466-6 gnd Stochastischer Prozess (DE-588)4057630-9 gnd
topic_facet	Analyse stochastique Martingales (mathématiques) Martingales (Mathematics) Stochastic analysis Stochastische Analysis Martingal Stochastischer Prozess
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007323888&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV010950028
work_keys_str_mv	AT yehjames martingalesandstochasticanalysis

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