Uniqueness for stochastic evolution equations in Banach spaces:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Warszawa
Polska Akad. Nauk, Inst. Matematyczny
2004
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| Schriftenreihe: | Dissertationes mathematicae
426 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 63 S. |
Internformat
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Datensatz im Suchindex
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| adam_text | 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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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T20:00:56Z |
| institution | BVB |
| language | English |
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| physical | 63 S. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
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| 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 Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Evolutionsgleichung (DE-588)4129061-6 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 Stochastische Differentialgleichung (DE-588)4057621-8 gnd Evolutionsgleichung (DE-588)4129061-6 gnd |
| subject_GND | (DE-588)4057621-8 (DE-588)4129061-6 |
| 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 Stochastische Differentialgleichung (DE-588)4057621-8 gnd Evolutionsgleichung (DE-588)4129061-6 gnd |
| topic_facet | Banach spaces Stochastic partial differential equations Stochastische Differentialgleichung Evolutionsgleichung |
| 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 |