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Malliavin calculus for processes with jumps:

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Bibliographic Details
Main Authors:	Bichteler, Klaus 1938- (Author), Gravereaux, Jean-Bernard (Author), Jacod, Jean 1944- (Author)
Format:	Book
Language:	English
Published:	New York [u.a.] Gordon and Breach 1987
Series:	Stochastics monographs 2
Subjects:	Analyse fonctionnelle Analyse stochastique Functional analysis Malliavin calculus Funktionalanalysis Diskreter stochastischer Prozess Stochastische Analysis Malliavin-Kalkül
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000546308&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Physical Description:	IX, 161 S.
ISBN:	2881241859

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MARC


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Record in the Search Index

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adam_text	CONTENTS Introduction to the Series vii Preface ix CHAPTER I Results 1 Section 1 Introduction 1 Section 2 The main results 6 2 a General setting and assumptions 6 2 b Existence of a density 10 2 c Regularity of the density 13 2 d Broad functions 16 Section 3 One example 19 CHAPTER II Techniques 25 Section 4 Toward existence and smoothness of the density for a random variable 26 4 a Integration by parts setting 27 4 b Iteration of the integration by parts formula 29 4 c Joint smoothness of the density 34 4 d More on joint smoothness 36 Section 5 Stability for stochastic differential equations 44 5 a Graded stochastic equations 45 5 b Differentiability 50 5 c Peano s approximation 54 CHAPTER III Bismut s Approach 59 Section 6 Calculus of variations 59 6 a The general setting 59 6 b The Girsanov transform 61 6 c Perturbation of the stochastic differential equation 65 6 d Explicit computation ofDX 70 vi CONTENTS 6 e Higher derivatives 72 6 f Integration by parts setting for X*t 76 Section 7 Proof of the main theorems via Bismut s approach 81 7 a Introductory remarks 81 7 b Existence of the density 82 7 c Smoothness of the density 91 CHAPTER IV MaUiavin s Approach 101 Section 8 Malliavin operators 101 8 a Definition of Malliavin operators 101 8 b Extension of Malliavin operators 104 8 c Malliavin operators on a direct product 108 Section 9 Malliavin operator on Wiener Poisson space 112 9 a Malliavin operator on Poisson space 112 9 b Malliavin operator on Wiener space 116 9 c Malliavin operator on Wiener Poisson space 117 9 d Malliavin operator and stochastic integrals 118 Section 10 Malliavin operator and stochastic differential equations 130 10 a The main result 130 10 b Explicit computation of U 140 10 c Application to existence and smoothness of the density 143 Section 11 Proof of the main theorems via MaUiavin s approach 147 11 a Introductory remarks 147 11 b Existence of the density 148 11 c Smoothness of the density 149 Section 12 Concluding remarks 150 References 155 Index 159 Notation 161
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author	Bichteler, Klaus 1938- Gravereaux, Jean-Bernard Jacod, Jean 1944-
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indexdate	2024-12-20T07:28:07Z
institution	BVB
isbn	2881241859
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-000546308
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physical	IX, 161 S.
publishDate	1987
publishDateSearch	1987
publishDateSort	1987
publisher	Gordon and Breach
record_format	marc
series	Stochastics monographs
series2	Stochastics monographs
spellingShingle	Bichteler, Klaus 1938- Gravereaux, Jean-Bernard Jacod, Jean 1944- Malliavin calculus for processes with jumps Stochastics monographs Analyse fonctionnelle Analyse fonctionnelle ram Analyse stochastique Functional analysis Malliavin calculus Funktionalanalysis (DE-588)4018916-8 gnd Diskreter stochastischer Prozess (DE-588)4150187-1 gnd Stochastische Analysis (DE-588)4132272-1 gnd Malliavin-Kalkül (DE-588)4242584-0 gnd
subject_GND	(DE-588)4018916-8 (DE-588)4150187-1 (DE-588)4132272-1 (DE-588)4242584-0
title	Malliavin calculus for processes with jumps
title_auth	Malliavin calculus for processes with jumps
title_exact_search	Malliavin calculus for processes with jumps
title_full	Malliavin calculus for processes with jumps Klaus Bichteler ; Jean-Bernard Gravereaux ; Jean Jacod
title_fullStr	Malliavin calculus for processes with jumps Klaus Bichteler ; Jean-Bernard Gravereaux ; Jean Jacod
title_full_unstemmed	Malliavin calculus for processes with jumps Klaus Bichteler ; Jean-Bernard Gravereaux ; Jean Jacod
title_short	Malliavin calculus for processes with jumps
title_sort	malliavin calculus for processes with jumps
topic	Analyse fonctionnelle Analyse fonctionnelle ram Analyse stochastique Functional analysis Malliavin calculus Funktionalanalysis (DE-588)4018916-8 gnd Diskreter stochastischer Prozess (DE-588)4150187-1 gnd Stochastische Analysis (DE-588)4132272-1 gnd Malliavin-Kalkül (DE-588)4242584-0 gnd
topic_facet	Analyse fonctionnelle Analyse stochastique Functional analysis Malliavin calculus Funktionalanalysis Diskreter stochastischer Prozess Stochastische Analysis Malliavin-Kalkül
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000546308&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000019799
work_keys_str_mv	AT bichtelerklaus malliavincalculusforprocesseswithjumps AT gravereauxjeanbernard malliavincalculusforprocesseswithjumps AT jacodjean malliavincalculusforprocesseswithjumps

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