The Malliavin calculus:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Harlow, Essex
Longman
1987
|
| Edition: | 1. publ. |
| Series: | Pitman monographs and surveys in pure and applied mathematics
34 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 105 S. |
| ISBN: | 0582994861 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV000727253 | ||
| 003 | DE-604 | ||
| 005 | 20160719 | ||
| 007 | t | ||
| 008 | 880328s1987 |||| 00||| eng d | ||
| 020 | |a 0582994861 |9 0-582-99486-1 | ||
| 035 | |a (OCoLC)14379466 | ||
| 035 | |a (DE-599)BVBBV000727253 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-384 |a DE-355 |a DE-739 |a DE-29T |a DE-83 |a DE-188 | ||
| 050 | 0 | |a QA274.2 | |
| 082 | 0 | |a 519.5 |2 19 | |
| 084 | |a SK 820 |0 (DE-625)143258: |2 rvk | ||
| 084 | |a 60H20 |2 msc | ||
| 084 | |a 28C20 |2 msc | ||
| 100 | 1 | |a Bell, Denis |e Verfasser |0 (DE-588)1036765539 |4 aut | |
| 245 | 1 | 0 | |a The Malliavin calculus |c Denis R. Bell |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Harlow, Essex |b Longman |c 1987 | |
| 300 | |a X, 105 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Pitman monographs and surveys in pure and applied mathematics |v 34 | |
| 650 | 4 | |a Analyse fonctionnelle | |
| 650 | 4 | |a Analyse stochastique | |
| 650 | 4 | |a Functional analysis | |
| 650 | 4 | |a Malliavin calculus | |
| 650 | 0 | 7 | |a Funktionalanalysis |0 (DE-588)4018916-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Stochastische Analysis |0 (DE-588)4132272-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Malliavin-Kalkül |0 (DE-588)4242584-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Stochastisches Integral |0 (DE-588)4126478-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Funktionalanalysis |0 (DE-588)4018916-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Stochastisches Integral |0 (DE-588)4126478-2 |D s |
| 689 | 1 | |5 DE-604 | |
| 689 | 2 | 0 | |a Malliavin-Kalkül |0 (DE-588)4242584-0 |D s |
| 689 | 2 | |5 DE-604 | |
| 689 | 3 | 0 | |a Stochastische Analysis |0 (DE-588)4132272-1 |D s |
| 689 | 3 | 1 | |a Funktionalanalysis |0 (DE-588)4018916-8 |D s |
| 689 | 3 | |5 DE-604 | |
| 830 | 0 | |a Pitman monographs and surveys in pure and applied mathematics |v 34 |w (DE-604)BV000022446 |9 34 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000454965&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-000454965 | ||
Record in the Search Index
| _version_ | 1804115178544955392 |
|---|---|
| adam_text | Contents
Preface ix
Introduction 1
1 Background material 7
1.1 Abstract Wiener spaces 7
1.2 Stochastic integration 10
1.3 Preliminary results 13
2 The functional analytic approach 16
2.1 Symmetric diffusion operators 16
2.2 A symmetric diffusion operator for Wiener space 20
2.3 Regularity of measures induced by Wiener functionals 26
2.4 Application of the Malliavin calculus to stochastic differential
equations 28
3 The variational approach 34
3.1 Perturbation via the Girsanov theorem 34
3.2 Smooth dependence of stochastic differential equations upon
parameters 37
3.3 Regularity of the measures induced by a stochastic differential
equation 41
4 An elementary derivation of Malliavin s inequalities 46
4.1 Introduction 46
4.2 A sequence of differentiable approximations to the It6 map 48
4.3 Derivation of the covariance matrix 53
4.4 Regularity of the measures induced by a stochastic differential
equation 56
vii
viii CONTENTS
5 A discussion of the different forms of the theory 63
5.1 An outline of Malliavin s original paper 63
5.2 A condition for equivalence of the approaches of Stroock and
Bismut 65
5.3 Transformation theorems and integration by parts operators 68
6 Non degeneracy of the covariance matrix under Hormander s
condition 73
6.1 Hormander s theorem 73
6.2 Hormander s condition implies o 1 e If for all p 11
7 Some further applications of the Malliavin calculus 87
7.1 The filtering problem 87
7.2 A study of an infinite system of interacting particles 92
7.3 Towards the construction of quasi invariant measures on an
infinite dimensional vector space 97
References 103
Index 105
|
| any_adam_object | 1 |
| author | Bell, Denis |
| author_GND | (DE-588)1036765539 |
| author_facet | Bell, Denis |
| author_role | aut |
| author_sort | Bell, Denis |
| author_variant | d b db |
| building | Verbundindex |
| bvnumber | BV000727253 |
| callnumber-first | Q - Science |
| callnumber-label | QA274 |
| callnumber-raw | QA274.2 |
| callnumber-search | QA274.2 |
| callnumber-sort | QA 3274.2 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 820 |
| ctrlnum | (OCoLC)14379466 (DE-599)BVBBV000727253 |
| dewey-full | 519.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 |
| dewey-search | 519.5 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02163nam a2200565 cb4500</leader><controlfield tag="001">BV000727253</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20160719 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">880328s1987 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0582994861</subfield><subfield code="9">0-582-99486-1</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)14379466</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV000727253</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA274.2</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519.5</subfield><subfield code="2">19</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 820</subfield><subfield code="0">(DE-625)143258:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">60H20</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">28C20</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Bell, Denis</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1036765539</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">The Malliavin calculus</subfield><subfield code="c">Denis R. Bell</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">1. publ.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Harlow, Essex</subfield><subfield code="b">Longman</subfield><subfield code="c">1987</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">X, 105 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Pitman monographs and surveys in pure and applied mathematics</subfield><subfield code="v">34</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Analyse fonctionnelle</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Analyse stochastique</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Functional analysis</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Malliavin calculus</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Funktionalanalysis</subfield><subfield code="0">(DE-588)4018916-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Stochastische Analysis</subfield><subfield code="0">(DE-588)4132272-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Malliavin-Kalkül</subfield><subfield code="0">(DE-588)4242584-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Stochastisches Integral</subfield><subfield code="0">(DE-588)4126478-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Funktionalanalysis</subfield><subfield code="0">(DE-588)4018916-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Stochastisches Integral</subfield><subfield code="0">(DE-588)4126478-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="2" ind2="0"><subfield code="a">Malliavin-Kalkül</subfield><subfield code="0">(DE-588)4242584-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="3" ind2="0"><subfield code="a">Stochastische Analysis</subfield><subfield code="0">(DE-588)4132272-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="3" ind2="1"><subfield code="a">Funktionalanalysis</subfield><subfield code="0">(DE-588)4018916-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="3" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Pitman monographs and surveys in pure and applied mathematics</subfield><subfield code="v">34</subfield><subfield code="w">(DE-604)BV000022446</subfield><subfield code="9">34</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000454965&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-000454965</subfield></datafield></record></collection> |
| id | DE-604.BV000727253 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:18:29Z |
| institution | BVB |
| isbn | 0582994861 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000454965 |
| oclc_num | 14379466 |
| open_access_boolean | |
| owner | DE-12 DE-384 DE-355 DE-BY-UBR DE-739 DE-29T DE-83 DE-188 |
| owner_facet | DE-12 DE-384 DE-355 DE-BY-UBR DE-739 DE-29T DE-83 DE-188 |
| physical | X, 105 S. |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | Longman |
| record_format | marc |
| series | Pitman monographs and surveys in pure and applied mathematics |
| series2 | Pitman monographs and surveys in pure and applied mathematics |
| spelling | Bell, Denis Verfasser (DE-588)1036765539 aut The Malliavin calculus Denis R. Bell 1. publ. Harlow, Essex Longman 1987 X, 105 S. txt rdacontent n rdamedia nc rdacarrier Pitman monographs and surveys in pure and applied mathematics 34 Analyse fonctionnelle Analyse stochastique Functional analysis Malliavin calculus Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Stochastische Analysis (DE-588)4132272-1 gnd rswk-swf Malliavin-Kalkül (DE-588)4242584-0 gnd rswk-swf Stochastisches Integral (DE-588)4126478-2 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 s DE-604 Stochastisches Integral (DE-588)4126478-2 s Malliavin-Kalkül (DE-588)4242584-0 s Stochastische Analysis (DE-588)4132272-1 s Pitman monographs and surveys in pure and applied mathematics 34 (DE-604)BV000022446 34 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000454965&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bell, Denis The Malliavin calculus Pitman monographs and surveys in pure and applied mathematics Analyse fonctionnelle Analyse stochastique Functional analysis Malliavin calculus Funktionalanalysis (DE-588)4018916-8 gnd Stochastische Analysis (DE-588)4132272-1 gnd Malliavin-Kalkül (DE-588)4242584-0 gnd Stochastisches Integral (DE-588)4126478-2 gnd |
| subject_GND | (DE-588)4018916-8 (DE-588)4132272-1 (DE-588)4242584-0 (DE-588)4126478-2 |
| title | The Malliavin calculus |
| title_auth | The Malliavin calculus |
| title_exact_search | The Malliavin calculus |
| title_full | The Malliavin calculus Denis R. Bell |
| title_fullStr | The Malliavin calculus Denis R. Bell |
| title_full_unstemmed | The Malliavin calculus Denis R. Bell |
| title_short | The Malliavin calculus |
| title_sort | the malliavin calculus |
| topic | Analyse fonctionnelle Analyse stochastique Functional analysis Malliavin calculus Funktionalanalysis (DE-588)4018916-8 gnd Stochastische Analysis (DE-588)4132272-1 gnd Malliavin-Kalkül (DE-588)4242584-0 gnd Stochastisches Integral (DE-588)4126478-2 gnd |
| topic_facet | Analyse fonctionnelle Analyse stochastique Functional analysis Malliavin calculus Funktionalanalysis Stochastische Analysis Malliavin-Kalkül Stochastisches Integral |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000454965&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000022446 |
| work_keys_str_mv | AT belldenis themalliavincalculus |