Malliavin calculus and its applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Mathematical Society
2009
|
| Series: | CBMS regional conference series in mathematics
110 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 85 S. |
| ISBN: | 9780821847794 |
Staff View
MARC
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| 300 | |a VIII, 85 S. | ||
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| 650 | 4 | |a Calculus of variations | |
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Record in the Search Index
| _version_ | 1804139189897265152 |
|---|---|
| adam_text | Contents
Preface
vu
Chapter
1.
The derivative operator
1
1.1.
Hermite polynomials and chaos expansions
1
1.2.
Derivative operator: Definition and properties
3
1.3.
Derivative in the white noise case
9
Chapter
2.
The divergence operator
13
2.1.
Properties of the divergence
13
2.2.
The divergence in the white noise case
15
2.3.
Clark-Ocone formula
17
Chapter
3.
The Ornstein-Uhlenbeck semigroup
19
3.1.
Mehler s formula
19
3.2.
Hypercontractivity
20
3.3.
The generator of the Ornstein-Uhlenbeck semigroup
23
Chapter
4.
Sobolev spaces and equivalence of norms
27
4.1.
Meyer inequalities
27
4.2.
A continuous family of seminorms and Sobolev spaces
29
4.3.
Continuity of the divergence
30
Chapter
5.
Regularity of probability laws
33
5.1.
Existence and formulas for probability densities
33
5.2.
Regularity of the density
35
Chapter
6.
Support properties. Density of the maximum
39
6.1.
Properties of the support of the law
39
6.2.
Regularity of the law of the maximum of continuous processes
40
Chapter
7.
Application of
Maffiavin
calculus to diffusion processes
45
7.1.
Differentiability of the solution
46
7.2.
Existence of densities under ellipticity conditions
48
7.3.
Regularity of the density under
Hörmander s
conditions
49
Chapter
8.
The divergence operator as a stochastic integral
55
8.1.
Skorohod integral
55
8.2.
Stochastic calculus for fractional Brownian motion
59
Chapter
9.
Central limit theorems and Malliavin calculus
67
9.1.
Central limit theorems via chaos expansions
67
9.2.
Stein s method and Malliavin calculus
72
vi
CONTENTS
Chapter
10.
Applications of Malliavin calculus in finance
75
10.1.
Black-Scholes model
75
10.2.
Computation of Greeks
76
10.3.
Application of the Clark-Ocone formula in hedging
80
Bibliography
81
Index
85
|
| any_adam_object | 1 |
| author | Nualart, David 1951- |
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| classification_rvk | SK 820 |
| ctrlnum | (OCoLC)488932483 (DE-599)BVBBV035547063 |
| 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.BV035547063 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:40:08Z |
| institution | BVB |
| isbn | 9780821847794 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017603030 |
| oclc_num | 488932483 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-188 |
| owner_facet | DE-355 DE-BY-UBR DE-188 |
| physical | VIII, 85 S. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | CBMS regional conference series in mathematics |
| series2 | CBMS regional conference series in mathematics |
| spelling | Nualart, David 1951- Verfasser (DE-588)113130902 aut Malliavin calculus and its applications David Nualart Providence, RI American Mathematical Society 2009 VIII, 85 S. txt rdacontent n rdamedia nc rdacarrier CBMS regional conference series in mathematics 110 Calculus of variations Malliavin calculus Malliavin-Kalkül (DE-588)4242584-0 gnd rswk-swf Malliavin-Kalkül (DE-588)4242584-0 s DE-604 CBMS regional conference series in mathematics 110 (DE-604)BV000004346 110 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017603030&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nualart, David 1951- Malliavin calculus and its applications CBMS regional conference series in mathematics Calculus of variations Malliavin calculus Malliavin-Kalkül (DE-588)4242584-0 gnd |
| subject_GND | (DE-588)4242584-0 |
| title | Malliavin calculus and its applications |
| title_auth | Malliavin calculus and its applications |
| title_exact_search | Malliavin calculus and its applications |
| title_full | Malliavin calculus and its applications David Nualart |
| title_fullStr | Malliavin calculus and its applications David Nualart |
| title_full_unstemmed | Malliavin calculus and its applications David Nualart |
| title_short | Malliavin calculus and its applications |
| title_sort | malliavin calculus and its applications |
| topic | Calculus of variations Malliavin calculus Malliavin-Kalkül (DE-588)4242584-0 gnd |
| topic_facet | Calculus of variations Malliavin calculus Malliavin-Kalkül |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017603030&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004346 |
| work_keys_str_mv | AT nualartdavid malliavincalculusanditsapplications |