Transition semigroups for stochastic semilinear equations on Hilbert spaces:
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| Format: | Buch |
| Sprache: | English |
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Warszawa
Inst. of Mathematics
2001
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| Schriftenreihe: | Dissertationes mathematicae
396 |
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| Beschreibung: | 59 S. |
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| 245 | 1 | 0 | |a Transition semigroups for stochastic semilinear equations on Hilbert spaces |c Anna Chojnowska-Michalik |
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Datensatz im Suchindex
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Titel: Transition semigroups for stochastic semilinear equations on Hilbert spaces
Autor: Chojnowska-Michalik, Anna
Jahr: 2001
CONTENTS
0. Introduction.5
Annotated contents .8
1. Preliminaries.9
2. The O-U semigroup (Rt) and Gaussian Sobolev spaces .13
2.1. Preliminaries—the semigroup (So(t)).14
2.2. The semigroups (Pf) and (Rt).1?
2.3. Sobolev spaces.18
2.4. Properties of L and (Rt).19
3. The semigroup (Pt) on Lp(H,fi)—existence for bounded F.23
3.1. Probabilistic approach.23
3.2. Analytic approach and equivalence .26
4. Properties of (Pt)—the case of bounded F.30
4.1. Hyperboundedness .30
4.2. Domains of generators.32
4.3. Invariant measures with densities .34
5. Examples.38
6. Logarithmic Sobolev inequality—the case of bounded F . . . .42
7. The semigroup (Pt)—the case of general .49
Appendix .35
References.37
Mathematics Subject Classification: 60H15, 47D07, 60J35, 47D06.
Key words and phrases: transition semigroups, stochastic semilinear equations, Girsanov trans-
form, hyperboundedness, Log Sobolev inequality, invariant measures.
Received 1.2.2000; revised 28.12.2000.
Abstract
A large class of stochastic semilinear equations with measurable nonlinear term on a Hilbert space
H is considered. Assuming the corresponding nonsymmetric Ornstein-Uhlenbeck process has an
invariant measure /x, we prove in the Lp(H,n) spaces the existence of a transition semigroup
(Pt) for the equations. Sufficient conditions are provided for hyperboundedness of Pt and for
the Log Sobolev Inequality to hold; and in the case of a bounded nonlinear term, sufficient and
necessary conditions are obtained. We prove the existence, uniqueness and some regularity of an
invariant density for (Pt). A characterization of the domain of the generator is also given. The
main tools are the Girsanov transform and Miyadera perturbations. |
| any_adam_object | 1 |
| author | Chojnowska-Michalik, Anna |
| author_facet | Chojnowska-Michalik, Anna |
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| author_sort | Chojnowska-Michalik, Anna |
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| indexdate | 2025-02-26T09:00:49Z |
| institution | BVB |
| language | English |
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| physical | 59 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
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| publisher | Inst. of Mathematics |
| record_format | marc |
| series | Dissertationes mathematicae |
| series2 | Dissertationes mathematicae |
| spelling | Chojnowska-Michalik, Anna Verfasser aut Transition semigroups for stochastic semilinear equations on Hilbert spaces Anna Chojnowska-Michalik Warszawa Inst. of Mathematics 2001 59 S. txt rdacontent n rdamedia nc rdacarrier Dissertationes mathematicae 396 Hilbert-Raum (DE-588)4159850-7 gnd rswk-swf Halbgruppe (DE-588)4022990-7 gnd rswk-swf Halbgruppe (DE-588)4022990-7 s Hilbert-Raum (DE-588)4159850-7 s DE-604 Dissertationes mathematicae 396 (DE-604)BV000003039 396 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009524043&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chojnowska-Michalik, Anna Transition semigroups for stochastic semilinear equations on Hilbert spaces Dissertationes mathematicae Hilbert-Raum (DE-588)4159850-7 gnd Halbgruppe (DE-588)4022990-7 gnd |
| subject_GND | (DE-588)4159850-7 (DE-588)4022990-7 |
| title | Transition semigroups for stochastic semilinear equations on Hilbert spaces |
| title_auth | Transition semigroups for stochastic semilinear equations on Hilbert spaces |
| title_exact_search | Transition semigroups for stochastic semilinear equations on Hilbert spaces |
| title_full | Transition semigroups for stochastic semilinear equations on Hilbert spaces Anna Chojnowska-Michalik |
| title_fullStr | Transition semigroups for stochastic semilinear equations on Hilbert spaces Anna Chojnowska-Michalik |
| title_full_unstemmed | Transition semigroups for stochastic semilinear equations on Hilbert spaces Anna Chojnowska-Michalik |
| title_short | Transition semigroups for stochastic semilinear equations on Hilbert spaces |
| title_sort | transition semigroups for stochastic semilinear equations on hilbert spaces |
| topic | Hilbert-Raum (DE-588)4159850-7 gnd Halbgruppe (DE-588)4022990-7 gnd |
| topic_facet | Hilbert-Raum Halbgruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009524043&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003039 |
| work_keys_str_mv | AT chojnowskamichalikanna transitionsemigroupsforstochasticsemilinearequationsonhilbertspaces |