A generalized parametrix method, smoothness of random fields and applications to parabolic stochastic partial differential equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Logos-Verl.
2001
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Zugl.: Mannheim, Univ., Diss., 2001. -Zsfassung in dt. Sprache |
| Beschreibung: | 115 S. |
| ISBN: | 3897227614 |
Internformat
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| 245 | 1 | 0 | |a A generalized parametrix method, smoothness of random fields and applications to parabolic stochastic partial differential equations |c vorgelegt von Susanne Kruse |
| 264 | 1 | |a Berlin |b Logos-Verl. |c 2001 | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Table
of
contents
Introduction
1.
Fundamental solutions for parabolic partial differential equations with
unbounded drift and potential
5
1.1
Formulation of the Cauchy problem
5
1.2
The Parametrix Method
7
1.3
Analytic properties of volume potentials
12
1.4
Construction of the fundamental solution
15
1.5
A solution to the Cauchy problem
28
1.6
Uniqueness of the solution to the Cauchy problem
33
2.
On sample function properties of random fields
35
2.1
^-Properties
35
2.2
Existence of separable, measurable modifications
39
2.3
Sample path continuity
40
2.4
Sample path differentiability
46
2.5
Sample path properties of Gaussian random fields
53
2.6
Conditions on the spectrum in the Gaussian case
57
2.7
Growth at infinity
63
3.
On the diffusion limit of diffusion-advection equations with a Gaussian
random field
71
3.1
The model and scaling of the stochastic partial differential equation
71
3.2
Weak convergence of the solution
74
Appendix
89
A. On the uniqueness of the solution to the Cauchy problem
89
B. Tightness of distribution valued processes
97
С
Miscellaneous
109
Bibliography
113
|
| adam_txt |
Table
of
contents
Introduction
1.
Fundamental solutions for parabolic partial differential equations with
unbounded drift and potential
5
1.1
Formulation of the Cauchy problem
5
1.2
The Parametrix Method
7
1.3
Analytic properties of volume potentials
12
1.4
Construction of the fundamental solution
15
1.5
A solution to the Cauchy problem
28
1.6
Uniqueness of the solution to the Cauchy problem
33
2.
On sample function properties of random fields
35
2.1
^-Properties
35
2.2
Existence of separable, measurable modifications
39
2.3
Sample path continuity
40
2.4
Sample path differentiability
46
2.5
Sample path properties of Gaussian random fields
53
2.6
Conditions on the spectrum in the Gaussian case
57
2.7
Growth at infinity
63
3.
On the diffusion limit of diffusion-advection equations with a Gaussian
random field
71
3.1
The model and scaling of the stochastic partial differential equation
71
3.2
Weak convergence of the solution
74
Appendix
89
A. On the uniqueness of the solution to the Cauchy problem
89
B. Tightness of distribution valued processes
97
С
Miscellaneous
109
Bibliography
113 |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| id | DE-604.BV021964091 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T16:08:43Z |
| indexdate | 2024-07-09T20:48:22Z |
| institution | BVB |
| isbn | 3897227614 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015179241 |
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| physical | 115 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
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| publisher | Logos-Verl. |
| record_format | marc |
| spelling | Kruse, Susanne Verfasser aut A generalized parametrix method, smoothness of random fields and applications to parabolic stochastic partial differential equations vorgelegt von Susanne Kruse Berlin Logos-Verl. 2001 115 S. txt rdacontent n rdamedia nc rdacarrier Zugl.: Mannheim, Univ., Diss., 2001. -Zsfassung in dt. Sprache Zufälliges Feld (DE-588)4191094-1 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Parabolische Differentialgleichung (DE-588)4173245-5 gnd rswk-swf Parametrix-Methode (DE-588)4499605-6 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Stochastische Differentialgleichung (DE-588)4057621-8 s DE-604 Parabolische Differentialgleichung (DE-588)4173245-5 s Zufälliges Feld (DE-588)4191094-1 s Parametrix-Methode (DE-588)4499605-6 s Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015179241&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kruse, Susanne A generalized parametrix method, smoothness of random fields and applications to parabolic stochastic partial differential equations Zufälliges Feld (DE-588)4191094-1 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd Parabolische Differentialgleichung (DE-588)4173245-5 gnd Parametrix-Methode (DE-588)4499605-6 gnd |
| subject_GND | (DE-588)4191094-1 (DE-588)4057621-8 (DE-588)4173245-5 (DE-588)4499605-6 (DE-588)4113937-9 |
| title | A generalized parametrix method, smoothness of random fields and applications to parabolic stochastic partial differential equations |
| title_auth | A generalized parametrix method, smoothness of random fields and applications to parabolic stochastic partial differential equations |
| title_exact_search | A generalized parametrix method, smoothness of random fields and applications to parabolic stochastic partial differential equations |
| title_exact_search_txtP | A generalized parametrix method, smoothness of random fields and applications to parabolic stochastic partial differential equations |
| title_full | A generalized parametrix method, smoothness of random fields and applications to parabolic stochastic partial differential equations vorgelegt von Susanne Kruse |
| title_fullStr | A generalized parametrix method, smoothness of random fields and applications to parabolic stochastic partial differential equations vorgelegt von Susanne Kruse |
| title_full_unstemmed | A generalized parametrix method, smoothness of random fields and applications to parabolic stochastic partial differential equations vorgelegt von Susanne Kruse |
| title_short | A generalized parametrix method, smoothness of random fields and applications to parabolic stochastic partial differential equations |
| title_sort | a generalized parametrix method smoothness of random fields and applications to parabolic stochastic partial differential equations |
| topic | Zufälliges Feld (DE-588)4191094-1 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd Parabolische Differentialgleichung (DE-588)4173245-5 gnd Parametrix-Methode (DE-588)4499605-6 gnd |
| topic_facet | Zufälliges Feld Stochastische Differentialgleichung Parabolische Differentialgleichung Parametrix-Methode Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015179241&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT krusesusanne ageneralizedparametrixmethodsmoothnessofrandomfieldsandapplicationstoparabolicstochasticpartialdifferentialequations |