Three classes of nonlinear stochastic partial differential equations:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey [u.a.]
World Scientific
2013
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Literaturverz. S. 157 - 162 |
| Physical Description: | XI, 164 S. |
| ISBN: | 9789814452359 9789814452366 |
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| 245 | 1 | 0 | |a Three classes of nonlinear stochastic partial differential equations |c Jie Xiong |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
vii
1.
Introduction
to Superprocesses
1
1.1
Branching particle system
.................. 1
1.2
The log-Laplace equation
.................. 7
1.3
The moment duality
..................... 8
1.4
The SPDE for the density
.................. 13
1.5
The SPDE for the distribution
............... 21
1.6
Historical remarks
...................... 22
2.
Superprocesses in Random Environments
25
2.1
Introduction and main result
................ 25
2.2
The moment duality
..................... 28
2.3
Conditional martingale problem
............... 30
2.4
Historical remarks
...................... 33
3.
Linear SPDE
35
3.1
An equation on measure space
............... 35
3.2
A duality representation
................... 44
3.3
Two estimates
........................ 53
3.4
Historical remarks
...................... 64
4.
Particle Representations for a Class of Nonlinear SPDEs
65
4.1
Introduction
.......................... 65
4.2
Solution for the system
................... 67
4.3
A nonlinear SPDE
...................... 79
IX
χ
Three Classes of Nonlinear Stochastic Partial Differential Equations
4.4
Historical remarks
...................... 80
5.
Stochastic Log-Laplace Equation
83
5.1
Introduction
.......................... 83
5.2
Approximation and two estimates
.............. 85
5.3
Existence and uniqueness
.................. 93
5.4
Conditional log-Laplace transform
............. 96
5.5
Historical remarks
...................... 104
6.
SPDEs for Density Fields of the Superprocesses
in Random Environment
105
6.1
Introduction
.......................... 105
6.2
Derivation of SPDE
..................... 108
6.3
A convolution representation
................
Ill
6.4
An estimate in spatial increment
.............. 114
6.5
Estimates in time increment
................. 116
6.6
Historical remarks
...................... 124
7.
Backward Doubly Stochastic Differential Equations
125
7.1
Introduction and basic definitions
.............. 125
7.2
Itô-Pardoux-Peng
formula
.................. 126
7.3
Uniqueness of solution
.................... 128
7.4
Historical remarks
...................... 130
8.
Prom SPDE to BSDE
131
8.1
The SPDE for the distribution
............... 131
8.2
Existence of solution to SPDE
............... 135
8.3
From BSDE to SPDE
.................... 141
8.4
Uniqueness for SPDE
.................... 143
8.5
Historical remarks
...................... 147
Appendix Some Auxiliary Results
149
A.I Martingale representation theorems
............. 149
A.
2
Weak convergence
...................... 154
A.3 Relation among strong existence, weak existence and path-
wise uniqueness
........................ 155
Contents xi
Bibliography
157
Index 163
Three Classes of Nonlinear Stochastic
Partial Differential Equations
The study of measure-valued processes in random environments
has seen some intensive research activities in recent years
whereby interesting nonlinear stochastic partial differential
equations (SPDEs) were derived. Due to the nonlinearity and the
non-Lipschitz continuity of their coefficients, new techniques
and concepts have recently been developed for the study of
such SPDEs. These include the conditional Laplace transform
technique, the conditional mild solution, and the bridge between
SPDEs and some kind of backward stochastic differential
equations. This volume provides an introduction to these topics
with the aim of attracting more researchers into this exciting and
young area of research. It can be considered as the first book
of its kind. The tools introduced and developed for the study of
measure-valued processes in random environments can be used
in a much
broaäer
area of nonlinear SPDEs.
ISBN
9Г8
981 4452 35 9
www.worldscientific.com
8728
he
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| id | DE-604.BV041153727 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:40:49Z |
| institution | BVB |
| isbn | 9789814452359 9789814452366 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026129140 |
| oclc_num | 864553158 |
| open_access_boolean | |
| owner | DE-703 DE-91G DE-BY-TUM |
| owner_facet | DE-703 DE-91G DE-BY-TUM |
| physical | XI, 164 S. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Xiong, Jie Verfasser aut Three classes of nonlinear stochastic partial differential equations Jie Xiong New Jersey [u.a.] World Scientific 2013 XI, 164 S. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 157 - 162 Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Stochastische nichtlineare Differentialgleichung (DE-588)4592295-0 gnd rswk-swf Stochastische nichtlineare Differentialgleichung (DE-588)4592295-0 s Partielle Differentialgleichung (DE-588)4044779-0 s DE-604 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026129140&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026129140&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Xiong, Jie Three classes of nonlinear stochastic partial differential equations Partielle Differentialgleichung (DE-588)4044779-0 gnd Stochastische nichtlineare Differentialgleichung (DE-588)4592295-0 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4592295-0 |
| title | Three classes of nonlinear stochastic partial differential equations |
| title_auth | Three classes of nonlinear stochastic partial differential equations |
| title_exact_search | Three classes of nonlinear stochastic partial differential equations |
| title_full | Three classes of nonlinear stochastic partial differential equations Jie Xiong |
| title_fullStr | Three classes of nonlinear stochastic partial differential equations Jie Xiong |
| title_full_unstemmed | Three classes of nonlinear stochastic partial differential equations Jie Xiong |
| title_short | Three classes of nonlinear stochastic partial differential equations |
| title_sort | three classes of nonlinear stochastic partial differential equations |
| topic | Partielle Differentialgleichung (DE-588)4044779-0 gnd Stochastische nichtlineare Differentialgleichung (DE-588)4592295-0 gnd |
| topic_facet | Partielle Differentialgleichung Stochastische nichtlineare Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026129140&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026129140&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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