A concise course on stochastic partial differential equations:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2007
|
| Series: | Lecture notes in mathematics
1905 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VI, 144 S. |
| ISBN: | 9783540707806 3540707808 |
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MARC
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| 100 | 1 | |a Prévôt, Claudia |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a A concise course on stochastic partial differential equations |c Claudia Prévôt ; Michael Röckner |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2007 | |
| 300 | |a VI, 144 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1905 | |
| 650 | 4 | |a Stochastische partielle Differentialgleichung | |
| 650 | 4 | |a Stochastic differential equations | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
1. Motivation,
Aims and Examples
1
2.
Stochastic Integral in Hubert Spaces
5
2.1.
Infinite-dimensional Wiener processes
.............. 5
2.2.
Martingales in general Banach spaces
............... 17
2.3.
The definition of the stochastic integral
............. 21
2.3.1.
Scheme of the construction of the stochastic integral
. . 22
2.3.2.
The construction of the stochastic integral
in detail
........................... 22
2.4.
Properties of the stochastic integral
................ 35
2.5.
The stochastic integral for cylindrical Wiener processes
.... 39
2.5.1.
Cylindrical Wiener processes
............... 39
2.5.2.
The definition of the stochastic integral
......... 41
3.
Stochastic Differential Equations in Finite Dimensions
43
3.1.
Main result and a localization lemma
............... 43
3.2.
Proof of existence and uniqueness
................. 49
4.
A Class of Stochastic Differential Equations
55
4.1.
Gelfand triples, conditions on the coefficients and examples
. . 55
4.2.
The main result and an
Ito
formula
................ 73
4.3.
Markov property and invariant measures
............. 91
A. The Bochner Integral
105
A.I. Definition of the Bochner integral
.................105
A.
2.
Properties of the Bochner integral
................107
B. Nuclear and
Hilbert-Schmidt
Operators
109
C.
Pseudo
Inverse of Linear Operators
115
D. Some Tools from Real Martingale Theory
119
E. Weak and Strong Solutions: Yamada-Watanabe Theorem
121
E.I. The main result
...........................121
F. Strong, Mild and Weak Solutions
133
VI
Contents
Bibliography iO
Index 140
Symbols 143
|
| adam_txt |
Contents
1. Motivation,
Aims and Examples
1
2.
Stochastic Integral in Hubert Spaces
5
2.1.
Infinite-dimensional Wiener processes
. 5
2.2.
Martingales in general Banach spaces
. 17
2.3.
The definition of the stochastic integral
. 21
2.3.1.
Scheme of the construction of the stochastic integral
. . 22
2.3.2.
The construction of the stochastic integral
in detail
. 22
2.4.
Properties of the stochastic integral
. 35
2.5.
The stochastic integral for cylindrical Wiener processes
. 39
2.5.1.
Cylindrical Wiener processes
. 39
2.5.2.
The definition of the stochastic integral
. 41
3.
Stochastic Differential Equations in Finite Dimensions
43
3.1.
Main result and a localization lemma
. 43
3.2.
Proof of existence and uniqueness
. 49
4.
A Class of Stochastic Differential Equations
55
4.1.
Gelfand triples, conditions on the coefficients and examples
. . 55
4.2.
The main result and an
Ito
formula
. 73
4.3.
Markov property and invariant measures
. 91
A. The Bochner Integral
105
A.I. Definition of the Bochner integral
.105
A.
2.
Properties of the Bochner integral
.107
B. Nuclear and
Hilbert-Schmidt
Operators
109
C.
Pseudo
Inverse of Linear Operators
115
D. Some Tools from Real Martingale Theory
119
E. Weak and Strong Solutions: Yamada-Watanabe Theorem
121
E.I. The main result
.121
F. Strong, Mild and Weak Solutions
133
VI
Contents
Bibliography iO
Index 140
Symbols 143 |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| index_date | 2024-07-02T17:44:19Z |
| indexdate | 2024-07-09T20:58:17Z |
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| isbn | 9783540707806 3540707808 |
| language | English |
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| series2 | Lecture notes in mathematics |
| spelling | Prévôt, Claudia Verfasser aut A concise course on stochastic partial differential equations Claudia Prévôt ; Michael Röckner Berlin [u.a.] Springer 2007 VI, 144 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1905 Stochastische partielle Differentialgleichung Stochastic differential equations Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd rswk-swf Stochastische partielle Differentialgleichung (DE-588)4135969-0 s DE-604 Röckner, Michael 1956- Verfasser (DE-588)121250199 aut Lecture notes in mathematics 1905 (DE-604)BV000676446 1905 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015677741&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Prévôt, Claudia Röckner, Michael 1956- A concise course on stochastic partial differential equations Lecture notes in mathematics Stochastische partielle Differentialgleichung Stochastic differential equations Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd |
| subject_GND | (DE-588)4135969-0 |
| title | A concise course on stochastic partial differential equations |
| title_auth | A concise course on stochastic partial differential equations |
| title_exact_search | A concise course on stochastic partial differential equations |
| title_exact_search_txtP | A concise course on stochastic partial differential equations |
| title_full | A concise course on stochastic partial differential equations Claudia Prévôt ; Michael Röckner |
| title_fullStr | A concise course on stochastic partial differential equations Claudia Prévôt ; Michael Röckner |
| title_full_unstemmed | A concise course on stochastic partial differential equations Claudia Prévôt ; Michael Röckner |
| title_short | A concise course on stochastic partial differential equations |
| title_sort | a concise course on stochastic partial differential equations |
| topic | Stochastische partielle Differentialgleichung Stochastic differential equations Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd |
| topic_facet | Stochastische partielle Differentialgleichung Stochastic differential equations |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015677741&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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