Holdings: Stochastic integration and differential equations

Stochastic integration and differential equations:

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Bibliographic Details
Main Author:	Protter, Philip E. 1949- (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] Springer 2004
Edition:	2. ed.
Series:	Applications of mathematics 21
Subjects:	Stochastic integrals Martingales (Mathematics) Stochastic differential equations Stochastisches Integral Stochastische Differentialgleichung Martingal
Online Access:	Inhaltsverzeichnis
Item Description:	Literaturverz. S. 389 - 401
Physical Description:	XIII, 415 S.
ISBN:	3540003134

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MARC


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Record in the Search Index

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adam_text	PHILIP E. PROTTER INTEGRATION S AND DIFFERENTIAL EQUATIONS SECOND EDITION SPRINGER CONTENTS INTRODUCTION 1 I PRELIMINARIES 3 1 BASIC DEFINITIONS AND NOTATION 3 2 MARTINGALES 7 3 THE POISSON PROCESS AND BRBWNIAN MOTION 12 4 LEVY PROCESSES 19 5 WHY THE USUAL HYPOTHESES? 34 6 LOCAL MARTINGALES 37 7 STIELTJES INTEGRATION AND CHANGE OF VARIABLES 39 8 NAIVE STOCHASTIC INTEGRATION IS IMPOSSIBLE 43 BIBLIOGRAPHIC NOTES 44 EXERCISES FOR CHAPTER I 45 II SEMIMARTINGALES AND STOCHASTIC INTEGRALS 51 1 INTRODUCTION TO SEMIMARTINGALES 51 2 STABILITY PROPERTIES OF SEMIMARTINGALES 52 3 ELEMENTARY EXAMPLES OF SEMIMARTINGALES 54 4 STOCHASTIC INTEGRALS 56 5 PROPERTIES OF STOCHASTIC INTEGRALS 60 6 THE QUADRATIC VARIATION OF A SEMIMARTINGALE 66 7 ITO S FORMULA (CHANGE OF VARIABLES) 78 8 APPLICATIONS OF ITO S FORMULA 84 BIBLIOGRAPHIC NOTES 92 EXERCISES FOR CHAPTER II 94 III SEMIMARTINGALES AND DECOMPOSABLE PROCESSES 101 1 INTRODUCTION 101 2 THE CLASSIFICATION OF STOPPING TIMES 103 3 THE DOOB-MEYER DECOMPOSITIONS 105 4 QUASIMARTINGALES 116 XII CONTENTS 5 COMPENSATORS 118 6 THE FUNDAMENTAL THEOREM OF LOCAL MARTINGALES 124 7 CLASSICAL SEMIMARTINGALES 127 8 GIRSANOV S THEOREM 131 9 THE BICHTELER-DELLACHERIE THEOREM 143 BIBLIOGRAPHIC NOTES 147 EXERCISES FOR CHAPTER III 147 IV GENERAL STOCHASTIC INTEGRATION AND LOCAL TIMES 153 1 INTRODUCTION 153 2 STOCHASTIC INTEGRATION FOR PREDICTABLE INTEGRANDS 153 3 MARTINGALE REPRESENTATION 178 4 MARTINGALE DUALITY AND THE JACOD-YOR THEOREM ON MARTINGALE REPRESENTATION 193 5 EXAMPLES OF MARTINGALE REPRESENTATION 200 6 STOCHASTIC INTEGRATION DEPENDING ON A PARAMETER 205 7 LOCAL TIMES 210 8 AZEMA S MARTINGALE 227 9 SIGMA MARTINGALES 233 BIBLIOGRAPHIC NOTES 235 EXERCISES FOR CHAPTER IV 236 V STOCHASTIC DIFFERENTIAL EQUATIONS 243 1 INTRODUCTION 243 2 THE HJ NORMS FOR SEMIMARTINGALES 244 3 EXISTENCE AND UNIQUENESS OF SOLUTIONS 249 4 STABILITY OF STOCHASTIC DIFFERENTIAL EQUATIONS 257 5 FISK-STRATONOVICH INTEGRALS AND DIFFERENTIAL EQUATIONS 270 6 THE MARKOV NATURE OF SOLUTIONS 291 7 FLOWS OF STOCHASTIC DIFFERENTIAL EQUATIONS: CONTINUITY AND DIFFERENTIABILITY 301 8 FLOWS AS DIFFEOMORPHISMS: THE CONTINUOUS CASE 310 9 GENERAL STOCHASTIC EXPONENTIALS AND LINEAR EQUATIONS 321 10 FLOWS AS DIFFEOMORPHISMS: THE GENERAL CASE . 32 8 11 ECLECTIC USEFUL RESULTS ON STOCHASTIC DIFFERENTIAL EQUATIONS ... 338 BIBLIOGRAPHIC NOTES 347 EXERCISES FOR CHAPTER V 349 VI EXPANSION OF FILTRATIONS 355 1 INTRODUCTION 355 2 INITIAL EXPANSIONS 356 3 PROGRESSIVE EXPANSIONS 369 4 TIME REVERSAL 377 BIBLIOGRAPHIC NOTES 383 EXERCISES FOR CHAPTER VI 384 CONTENTS XIII REFERENCES 389 SYMBOL INDEX 403 SUBJECT INDEX 407
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author	Protter, Philip E. 1949-
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ctrlnum	(OCoLC)248898805 (DE-599)BVBBV016523843
dewey-full	519.2 519.222
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dewey-search	519.2 519.2 22
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discipline	Mathematik
edition	2. ed.
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indexdate	2024-07-09T19:11:31Z
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isbn	3540003134
language	English
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physical	XIII, 415 S.
publishDate	2004
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publisher	Springer
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series	Applications of mathematics
series2	Applications of mathematics
spelling	Protter, Philip E. 1949- Verfasser (DE-588)121454304 aut Stochastic integration and differential equations Philip E. Protter 2. ed. Berlin [u.a.] Springer 2004 XIII, 415 S. txt rdacontent n rdamedia nc rdacarrier Applications of mathematics 21 Literaturverz. S. 389 - 401 Stochastic integrals Martingales (Mathematics) Stochastic differential equations Stochastisches Integral (DE-588)4126478-2 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Martingal (DE-588)4126466-6 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 s DE-604 Martingal (DE-588)4126466-6 s Stochastisches Integral (DE-588)4126478-2 s Applications of mathematics 21 (DE-604)BV000895226 21 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010211629&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Protter, Philip E. 1949- Stochastic integration and differential equations Applications of mathematics Stochastic integrals Martingales (Mathematics) Stochastic differential equations Stochastisches Integral (DE-588)4126478-2 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd Martingal (DE-588)4126466-6 gnd
subject_GND	(DE-588)4126478-2 (DE-588)4057621-8 (DE-588)4126466-6
title	Stochastic integration and differential equations
title_auth	Stochastic integration and differential equations
title_exact_search	Stochastic integration and differential equations
title_full	Stochastic integration and differential equations Philip E. Protter
title_fullStr	Stochastic integration and differential equations Philip E. Protter
title_full_unstemmed	Stochastic integration and differential equations Philip E. Protter
title_short	Stochastic integration and differential equations
title_sort	stochastic integration and differential equations
topic	Stochastic integrals Martingales (Mathematics) Stochastic differential equations Stochastisches Integral (DE-588)4126478-2 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd Martingal (DE-588)4126466-6 gnd
topic_facet	Stochastic integrals Martingales (Mathematics) Stochastic differential equations Stochastisches Integral Stochastische Differentialgleichung Martingal
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010211629&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000895226
work_keys_str_mv	AT protterphilipe stochasticintegrationanddifferentialequations

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