Malliavin calculus for processes with jumps:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Gordon and Breach
1987
|
| Series: | Stochastics monographs
2 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 161 S. |
| ISBN: | 2881241859 |
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MARC
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| 245 | 1 | 0 | |a Malliavin calculus for processes with jumps |c Klaus Bichteler ; Jean-Bernard Gravereaux ; Jean Jacod |
| 264 | 1 | |a New York [u.a.] |b Gordon and Breach |c 1987 | |
| 300 | |a IX, 161 S. | ||
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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
|
| any_adam_object | 1 |
| author | Bichteler, Klaus 1938- Gravereaux, Jean-Bernard Jacod, Jean 1944- |
| author_GND | (DE-588)106060279 (DE-588)140772421 |
| author_facet | Bichteler, Klaus 1938- Gravereaux, Jean-Bernard Jacod, Jean 1944- |
| author_role | aut aut aut |
| author_sort | Bichteler, Klaus 1938- |
| author_variant | k b kb j b g jbg j j jj |
| building | Verbundindex |
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| ctrlnum | (OCoLC)14967382 (DE-599)BVBBV000869994 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV000869994 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:20:47Z |
| institution | BVB |
| isbn | 2881241859 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000546308 |
| oclc_num | 14967382 |
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| owner | DE-12 DE-384 DE-91G DE-BY-TUM DE-739 DE-355 DE-BY-UBR DE-824 DE-29T DE-706 DE-188 |
| owner_facet | DE-12 DE-384 DE-91G DE-BY-TUM DE-739 DE-355 DE-BY-UBR DE-824 DE-29T DE-706 DE-188 |
| physical | IX, 161 S. |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | Gordon and Breach |
| record_format | marc |
| series | Stochastics monographs |
| series2 | Stochastics monographs |
| spelling | Bichteler, Klaus 1938- Verfasser (DE-588)106060279 aut Malliavin calculus for processes with jumps Klaus Bichteler ; Jean-Bernard Gravereaux ; Jean Jacod New York [u.a.] Gordon and Breach 1987 IX, 161 S. txt rdacontent n rdamedia nc rdacarrier Stochastics monographs 2 Analyse fonctionnelle Analyse fonctionnelle ram Analyse stochastique Functional analysis Malliavin calculus Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Diskreter stochastischer Prozess (DE-588)4150187-1 gnd rswk-swf Stochastische Analysis (DE-588)4132272-1 gnd rswk-swf Malliavin-Kalkül (DE-588)4242584-0 gnd rswk-swf Malliavin-Kalkül (DE-588)4242584-0 s DE-604 Diskreter stochastischer Prozess (DE-588)4150187-1 s Funktionalanalysis (DE-588)4018916-8 s Stochastische Analysis (DE-588)4132272-1 s Gravereaux, Jean-Bernard Verfasser aut Jacod, Jean 1944- Verfasser (DE-588)140772421 aut Stochastics monographs 2 (DE-604)BV000019799 2 HBZ Datenaustausch application/pdf 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 Inhaltsverzeichnis |
| 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 |
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