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Bibliographic Details
Main Author:	Protter, Philip E. 1949- (Author)
Format:	Book
Language:	English
Published:	Berlin ; Heidelberg Springer [2005]
Edition:	Second edition, Version 2.1, corrected 3rd. printing
Series:	Stochastic modelling and applied probability 21
Subjects:	Stochastische Differentialgleichung Stochastisches Integral Martingal
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013345061&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Item Description:	Hier auch später erschienene, unveränderte Nachdrucke
Physical Description:	xiii, 419 Seiten
ISBN:	9783642055607 9783540003137 3540003134

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adam_text	Contents Introduction ................................................... 1 I Preliminaries .............................................. З 1 Basic Definitions and Notation ............................ 3 2 Martingales ............................................. 7 3 The Poisson Process and Brownian Motion ................. 12 4 Levy Processes .......................................... 20 5 Why the Usual Hypotheses? .............................. 34 6 Local Martingales ....................................... 37 7 Stieltjes Integration and Change of Variables ................ 39 8 Naïve 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 Itô s Formula (Change of Variables) ........................ 78 8 Applications of Itô 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 .......................104 3 The Doob-Meyer Decompositions ..........................106 4 Quasimartingales ........................................117 5 Compensators ...........................................119 6 The Fundamental Theorem of Local Martingales ............126 7 Classical Semimartingales ................................129 8 Girsanov s Theorem .....................................133 9 The Bichteler-Dellacherie Theorem ........................146 Bibliographic Notes ..........................................149 Exercises for Chapter III ......................................150 IV General Stochastic Integration and Local Times ...........155 1 Introduction ............................................155 2 Stochastic Integration for Predictable Integrands ............155 3 Martingale Representation ................................180 4 Martingale Duality and the Jacod-Yor Theorem on Martingale Representation ................................195 5 Examples of Martingale Representation ....................203 6 Stochastic Integration Depending on a Parameter ............208 7 Local Times ............................................213 8 Azéma s Martingale ......................................232 9 Sigma Martingales .......................................237 Bibliographic Notes ..........................................240 Exercises for Chapter IV ......................................241 V Stochastic Differential Equations ..........................249 1 Introduction ............................................249 2 The H_p Norms for Semimartingales ........................250 3 Existence and Uniqueness of Solutions .....................255 4 Stability of Stochastic Differential Equations ................263 5 Fisk-Stratonovich Integrals and Differential Equations ........277 6 The Markov Nature of Solutions ...........................297 7 Flows of Stochastic Differential Equations: Continuity and Differentiability .........................................307 8 Flows as Diffeomorphisms: The Continuous Case ............317 9 General Stochastic Exponentials and Linear Equations .......328 10 Flows as Diffeomorphisms: The General Case ...............335 11 Eclectic Useful Results on Stochastic Differential Equations ... 345 Bibliographic Notes ..........................................354 Exercises for Chapter V ......................................355 VI Expansion of Filtrations ...................................363 1 Introduction ............................................363 2 Initial Expansions .......................................364 3 Progressive Expansions ...................................378 4 Time Reversal ..........................................385 Bibliographic Notes ..........................................391 Exercises for Chapter VI ......................................392 References .....................................................397 Subject Index .................................................411
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edition	Second edition, Version 2.1, corrected 3rd. printing
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isbn	9783642055607 9783540003137 3540003134
language	English
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physical	xiii, 419 Seiten
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series	Stochastic modelling and applied probability
series2	Stochastic modelling and applied probability
spellingShingle	Protter, Philip E. 1949- Stochastic integration and differential equations Stochastic modelling and applied probability Stochastische Differentialgleichung (DE-588)4057621-8 gnd Stochastisches Integral (DE-588)4126478-2 gnd Martingal (DE-588)4126466-6 gnd
subject_GND	(DE-588)4057621-8 (DE-588)4126478-2 (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	Stochastische Differentialgleichung (DE-588)4057621-8 gnd Stochastisches Integral (DE-588)4126478-2 gnd Martingal (DE-588)4126466-6 gnd
topic_facet	Stochastische Differentialgleichung Stochastisches Integral Martingal
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013345061&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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work_keys_str_mv	AT protterphilipe stochasticintegrationanddifferentialequations

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