Uniqueness for stochastic evolution equations in Banach spaces:
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| Format: | Book |
| Language: | English |
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Warszawa
Polska Akad. Nauk, Inst. Matematyczny
2004
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| Series: | Dissertationes mathematicae
426 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 63 S. |
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Record in the Search Index
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Titel: Uniqueness for stochastic evolution equations in Banach spaces
Autor: Ondreját, Martin
Jahr: 2004
CONTENTS
Introduction .5
1. Cylindrical Wiener process.16
2. Radonifying mappings and the space Uq. 18
3. Stochastic integral.21
4. A convergence result.28
5. Burkholder inequality.28
6. Fubini's theorem. 30
7. The Girsanov theorem.35
8. Distribution of random integrals and measurable selectors
9. Proofs of Theorems 3 and 4.
10. Proofs of Theorems 5 and 6.
11. Preliminaries to the proofs of Theorems 1 and 2.
12. Proof of Theorem 2.
13. Proof of Theorem 1.
14. Proofs of Theorems 8, 9 and 10.
References.
Abstract
Different types of uniqueness (e.g. pathwise uniqueness, uniqueness in law, joint uniqueness in
law) and existence (e.g. strong solution, martingale solution) for stochastic evolution equations
driven by a Wiener process are studied and compared. We show a sufficient condition for a joint
distribution of a process and a Wiener process to be a solution of a given SPDE. Equivalences
between different concepts of solution are shown. An alternative approach to the construction of
the stochastic integral in 2-smooth Banach spaces is included as well as Burkholder s inequality,
stochastic Fubini's theorem and the Girsanov theorem.
2000 Mathematics Subject Classification: Primary 60H15. ;iiq7
This research was supported in part by the GA CR Grant o.
Received 24.1.2003; revised 29.12.2003- |
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| indexdate | 2025-03-31T20:04:13Z |
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| language | English |
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| physical | 63 S. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Polska Akad. Nauk, Inst. Matematyczny |
| record_format | marc |
| series | Dissertationes mathematicae |
| series2 | Dissertationes mathematicae |
| spelling | Ondreját, Martin Verfasser aut Uniqueness for stochastic evolution equations in Banach spaces Martin Ondreját Warszawa Polska Akad. Nauk, Inst. Matematyczny 2004 63 S. txt rdacontent n rdamedia nc rdacarrier Dissertationes mathematicae 426 Banach spaces Stochastic partial differential equations Evolutionsgleichung (DE-588)4129061-6 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Evolutionsgleichung (DE-588)4129061-6 s Stochastische Differentialgleichung (DE-588)4057621-8 s DE-604 Dissertationes mathematicae 426 (DE-604)BV000003039 426 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012925625&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ondreját, Martin Uniqueness for stochastic evolution equations in Banach spaces Dissertationes mathematicae Banach spaces Stochastic partial differential equations Evolutionsgleichung (DE-588)4129061-6 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
| subject_GND | (DE-588)4129061-6 (DE-588)4057621-8 |
| title | Uniqueness for stochastic evolution equations in Banach spaces |
| title_auth | Uniqueness for stochastic evolution equations in Banach spaces |
| title_exact_search | Uniqueness for stochastic evolution equations in Banach spaces |
| title_full | Uniqueness for stochastic evolution equations in Banach spaces Martin Ondreját |
| title_fullStr | Uniqueness for stochastic evolution equations in Banach spaces Martin Ondreját |
| title_full_unstemmed | Uniqueness for stochastic evolution equations in Banach spaces Martin Ondreját |
| title_short | Uniqueness for stochastic evolution equations in Banach spaces |
| title_sort | uniqueness for stochastic evolution equations in banach spaces |
| topic | Banach spaces Stochastic partial differential equations Evolutionsgleichung (DE-588)4129061-6 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
| topic_facet | Banach spaces Stochastic partial differential equations Evolutionsgleichung Stochastische Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012925625&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003039 |
| work_keys_str_mv | AT ondrejatmartin uniquenessforstochasticevolutionequationsinbanachspaces |