Degenerate stochastic differential equations and hypoellipticity:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Harlow
Longman
1995
|
| Edition: | 1. publ. |
| Series: | Pitman monographs and surveys in pure and applied mathematics
79 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 114 S. |
| ISBN: | 058224689X |
Staff View
MARC
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| 100 | 1 | |a Bell, Denis R. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Degenerate stochastic differential equations and hypoellipticity |c Denis R. Bell |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Harlow |b Longman |c 1995 | |
| 300 | |a VIII, 114 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 79 | |
| 650 | 7 | |a Equations différentielles stochastiques |2 ram | |
| 650 | 7 | |a théorème Hörmander |2 inriac | |
| 650 | 7 | |a équation différentielle stochastique |2 inriac | |
| 650 | 7 | |a équation hypoelliptique |2 inriac | |
| 650 | 4 | |a Stochastic differential equations | |
| 650 | 0 | 7 | |a Stochastische Differentialgleichung |0 (DE-588)4057621-8 |2 gnd |9 rswk-swf |
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Record in the Search Index
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| adam_text | Contents
Preface ix
List of notations xi
Introduction 1
1 Background material 4
1.1 The Wiener space 4
1.1.1 Brownian motion 4
1.1.2 Wiener s theorem 5
1.1.3 Abstract Wiener spaces 9
1.2 Stochastic integration 11
1.2.1 Construction of the Ito integral 12
1.2.2 Computation of a stochastic integral 14
1.2.3 The multidimensional Ito integral and its properties 15
1.3 Stochastic differential equations 18
1.3.1 Existence and uniqueness of solutions 18
1.3.2 The Kolmogorov equations 21
1.4 Criteria for the regularity of a Borel measure 23
2 Regularity of measures induced by stochastic
differential equations 26
2.1 A finite dimensional analogue of the regularity problem 26
2.2 The Malliavin calculus 27
2.2.1 A summary of Malliavin s paper 27
2.2.2 Stroock s functional analytic formulation 30
2.3 An elementary proof of the Malliavin Stroock theorem 31
2.3.1 Motivation 31
2.3.2 A sequence of differentiable approximations to the Ito map 32
2.3.3 Derivation of the covariance martrix 36
2.3.4 The regularity theorems 39
3 The probabilistic form of Hormander s theorem 47
3.1 Existence of densities under Hormander s condition 47
3.2 Smoothness of densities under Hormander s condition 50
viii
4 Infinitely degenerate hypoelliptic operators 59
4.1 An extension of Hormander s theorem 59
4.2 Regularity of the heat semigroup 63
4.3 Proofs of the Theorems 65
4.4 Lower bounds for degenerate ltd processes 70
5 Smooth densities for a class of stochastic functional
equations 78
5.1 Stochastic hereditary delay equations 78
5.2 Statement of hypotheses and theorems 79
5.3 Analysis of the conditioned equation 83
5.4 Proof of the main theorem 91
6 Generalized divergence operators and absolutely continuous
transformations 98
6.1 Transformations of Gaussian measure 98
6.2 A formula for a class of Radon Nikodym derivatives 100
6.3 Differentiable and quasi invariant measures 103
References 112
|
| any_adam_object | 1 |
| author | Bell, Denis R. |
| author_facet | Bell, Denis R. |
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| classification_tum | MAT 606f |
| ctrlnum | (OCoLC)34113807 (DE-599)BVBBV010715171 |
| 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 |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV010715171 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:57:42Z |
| institution | BVB |
| isbn | 058224689X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007154895 |
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| physical | VIII, 114 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| 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 R. Verfasser aut Degenerate stochastic differential equations and hypoellipticity Denis R. Bell 1. publ. Harlow Longman 1995 VIII, 114 S. txt rdacontent n rdamedia nc rdacarrier Pitman monographs and surveys in pure and applied mathematics 79 Equations différentielles stochastiques ram théorème Hörmander inriac équation différentielle stochastique inriac équation hypoelliptique inriac Stochastic differential equations Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 s DE-604 Pitman monographs and surveys in pure and applied mathematics 79 (DE-604)BV000022446 79 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007154895&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bell, Denis R. Degenerate stochastic differential equations and hypoellipticity Pitman monographs and surveys in pure and applied mathematics Equations différentielles stochastiques ram théorème Hörmander inriac équation différentielle stochastique inriac équation hypoelliptique inriac Stochastic differential equations Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
| subject_GND | (DE-588)4057621-8 |
| title | Degenerate stochastic differential equations and hypoellipticity |
| title_auth | Degenerate stochastic differential equations and hypoellipticity |
| title_exact_search | Degenerate stochastic differential equations and hypoellipticity |
| title_full | Degenerate stochastic differential equations and hypoellipticity Denis R. Bell |
| title_fullStr | Degenerate stochastic differential equations and hypoellipticity Denis R. Bell |
| title_full_unstemmed | Degenerate stochastic differential equations and hypoellipticity Denis R. Bell |
| title_short | Degenerate stochastic differential equations and hypoellipticity |
| title_sort | degenerate stochastic differential equations and hypoellipticity |
| topic | Equations différentielles stochastiques ram théorème Hörmander inriac équation différentielle stochastique inriac équation hypoelliptique inriac Stochastic differential equations Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
| topic_facet | Equations différentielles stochastiques théorème Hörmander équation différentielle stochastique équation hypoelliptique Stochastic differential equations Stochastische Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007154895&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000022446 |
| work_keys_str_mv | AT belldenisr degeneratestochasticdifferentialequationsandhypoellipticity |