A minicourse on stochastic partial differential equations:
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| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2009
|
| Series: | Lecture notes in mathematics
1962 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XI, 216 S. |
| ISBN: | 9783540859932 ebook 9783540859949 |
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| 245 | 1 | 0 | |a A minicourse on stochastic partial differential equations |c Robert Dalang ... Ed.: Davar Khoshnevisan ... |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2009 | |
| 300 | |a XI, 216 S. | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
A Primer on Stochastic Partial Differential Equations
Davar Khoshnevisan
.............................................. 1
1
What is an SPDE?
......................................... 1
2
Gaussian Random Vectors
................................... 2
3
Gaussian Processes
......................................... 2
4
Regularity of Random Processes
.............................. 8
5
Martingale Measures
........................................ 14
6
A Nonlinear Heat Equation
.................................. 23
7
Prom Chaos to Order
....................................... 32
References
...................................................... 36
The Stochastic Wave Equation
Robert C. Dalang
................................................ 39
1
Introduction
............................................... 39
2
The Stochastic Wave Equation
............................... 41
3
Spatially Homogeneous Gaussian Noise
........................ 47
4
The Wave Equation in Spatial Dimension
2.................... 49
5
A Function-Valued Stochastic Integral
........................ 56
6
The Wave Equation in Spatial Dimension
d
> 1................ 58
7
Spatial Regularity of the Stochastic Integral (d
= 3) ............ 61
8
Holder-Continuity in the 3-d Wave Equation
................... 70
References
...................................................... 71
Application of Malliavin Calculus to Stochastic Partial
Differential Equations
David Nualart
................................................... 73
1
Introduction
............................................... 73
2
Malliavin Calculus
.......................................... 73
3
Application of Malliavin Calculus to Regularity
of Probability Laws
......................................... 83
4
Stochastic Heat Equation
.................................... 92
IX
X Contents
5
Spatially Homogeneous SPDEs
............................... 99
References
......................................................108
Some Tools and Results for Parabolic Stochastic Partial
Differential Equations
Carl Mueller
....................................................
Ill
1
Introduction
...............................................
Ill
2
Basic Framework
...........................................113
3
Duality
...................................................115
4
Large Deviations for SPDEs
.................................125
5
A Comparison Theorem
.....................................129
6
Applications
...............................................131
References
......................................................142
Sample Path Properties of
Anisotropie
Gaussian Random
Fields
Yimin Xiao
.....................................................145
1
Introduction
...............................................145
2
Examples and General Assumptions
..........................148
3
Properties of Strong Local Nondeterminism
....................160
4
Modulus of Continuity
......................................164
5
Small Ball Probabilities
.....................................168
6
Hausdorff and Packing Dimensions of the Range and Graph
.....170
7
Hausdorff Dimension of the Level Sets and Hitting Probabilities
.. 183
8
Local Times and Their Joint Continuity
......................194
References
......................................................207
List of Participants
............................................213
Index
..........................................................215
|
| adam_txt |
Contents
A Primer on Stochastic Partial Differential Equations
Davar Khoshnevisan
. 1
1
What is an SPDE?
. 1
2
Gaussian Random Vectors
. 2
3
Gaussian Processes
. 2
4
Regularity of Random Processes
. 8
5
Martingale Measures
. 14
6
A Nonlinear Heat Equation
. 23
7
Prom Chaos to Order
. 32
References
. 36
The Stochastic Wave Equation
Robert C. Dalang
. 39
1
Introduction
. 39
2
The Stochastic Wave Equation
. 41
3
Spatially Homogeneous Gaussian Noise
. 47
4
The Wave Equation in Spatial Dimension
2. 49
5
A Function-Valued Stochastic Integral
. 56
6
The Wave Equation in Spatial Dimension
d
> 1. 58
7
Spatial Regularity of the Stochastic Integral (d
= 3) . 61
8
Holder-Continuity in the 3-d Wave Equation
. 70
References
. 71
Application of Malliavin Calculus to Stochastic Partial
Differential Equations
David Nualart
. 73
1
Introduction
. 73
2
Malliavin Calculus
. 73
3
Application of Malliavin Calculus to Regularity
of Probability Laws
. 83
4
Stochastic Heat Equation
. 92
IX
X Contents
5
Spatially Homogeneous SPDEs
. 99
References
.108
Some Tools and Results for Parabolic Stochastic Partial
Differential Equations
Carl Mueller
.
Ill
1
Introduction
.
Ill
2
Basic Framework
.113
3
Duality
.115
4
Large Deviations for SPDEs
.125
5
A Comparison Theorem
.129
6
Applications
.131
References
.142
Sample Path Properties of
Anisotropie
Gaussian Random
Fields
Yimin Xiao
.145
1
Introduction
.145
2
Examples and General Assumptions
.148
3
Properties of Strong Local Nondeterminism
.160
4
Modulus of Continuity
.164
5
Small Ball Probabilities
.168
6
Hausdorff and Packing Dimensions of the Range and Graph
.170
7
Hausdorff Dimension of the Level Sets and Hitting Probabilities
. 183
8
Local Times and Their Joint Continuity
.194
References
.207
List of Participants
.213
Index
.215 |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| indexdate | 2024-07-09T21:23:11Z |
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| isbn | 9783540859932 ebook 9783540859949 |
| language | English |
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| physical | XI, 216 S. |
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| spelling | A minicourse on stochastic partial differential equations Robert Dalang ... Ed.: Davar Khoshnevisan ... Berlin [u.a.] Springer 2009 XI, 216 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1962 Literaturangaben Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2006 Salt Lake City Utah gnd-content Stochastische partielle Differentialgleichung (DE-588)4135969-0 s DE-604 Dalang, Robert C. 1961- Sonstige (DE-588)120870878 oth Khoshnevisan, Davar 1964- Sonstige (DE-588)124139795 oth Lecture notes in mathematics 1962 (DE-604)BV000676446 1962 http://d-nb.info/990909158/04 Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016807425&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | A minicourse on stochastic partial differential equations Lecture notes in mathematics Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd |
| subject_GND | (DE-588)4135969-0 (DE-588)1071861417 |
| title | A minicourse on stochastic partial differential equations |
| title_auth | A minicourse on stochastic partial differential equations |
| title_exact_search | A minicourse on stochastic partial differential equations |
| title_exact_search_txtP | A minicourse on stochastic partial differential equations |
| title_full | A minicourse on stochastic partial differential equations Robert Dalang ... Ed.: Davar Khoshnevisan ... |
| title_fullStr | A minicourse on stochastic partial differential equations Robert Dalang ... Ed.: Davar Khoshnevisan ... |
| title_full_unstemmed | A minicourse on stochastic partial differential equations Robert Dalang ... Ed.: Davar Khoshnevisan ... |
| title_short | A minicourse on stochastic partial differential equations |
| title_sort | a minicourse on stochastic partial differential equations |
| topic | Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd |
| topic_facet | Stochastische partielle Differentialgleichung Konferenzschrift 2006 Salt Lake City Utah |
| url | http://d-nb.info/990909158/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016807425&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT dalangrobertc aminicourseonstochasticpartialdifferentialequations AT khoshnevisandavar aminicourseonstochasticpartialdifferentialequations |
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