Existence and uniqueness results for semilinear stochastic partial differential equations

被引：132

作者：

Gyongy, I ^{[1
]}

机构：

[1] Univ Edinburgh, Dept Math & Stat, Edinburgh EH9 3JZ, Midlothian, Scotland

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 1998年 / 73卷 / 02期

关键词：

stochastic partial differential equations; space-time white noise; green measures;

D O I：

10.1016/S0304-4149(97)00103-8

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We prove existence, uniqueness and comparison theorems for a class of semilinear stochastic partial differential equations driven by space-time white noise. The class of equations we investigate contains as special cases the stochastic Burgers equation and the reaction-diffusion equations perturbed by space-time white noise. (C) 1998 Elsevier Science B.V. All rights reserved.

引用

页码：271 / 299

页数：29

共 23 条

[1] [Anonymous], 1995, STOCH STOCH REP, DOI DOI 10.1080/17442509508833962
[2] WHITE-NOISE DRIVEN PARABOLIC SPDES WITH MEASURABLE DRIFT
BALLY, V
GYONGY, I
PARDOUX, E
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1994, 120 (02) : 484 - 510
[3] BERTINI L, 1995, STOCHASTIC BURGERS E
[4] Burgers J M, 1974, NONLINEAR DIFFUSION, DOI DOI 10.1007/978-94-010-1745-9
[5] DEPRATO G, 1995, STOCHASTIC BURGERS E
[6] WHITE-NOISE DRIVEN SPDES WITH REFLECTION
DONATIMARTIN, C
PARDOUX, E
[J]. PROBABILITY THEORY AND RELATED FIELDS, 1993, 95 (01) : 1 - 24
[7] RANDOM MOTION OF STRINGS AND RELATED STOCHASTIC-EVOLUTION EQUATIONS
FUNAKI, T
[J]. NAGOYA MATHEMATICAL JOURNAL, 1983, 89 (MAR) : 129 - 193
[8] REAL VARIABLE LEMMA AND CONTINUITY OF PATHS OF SOME GAUSSIAN PROCESSES
GARSIA, AM
RODEMICH, E
RUMSEY, H
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1970, 20 (06) : 565 - &
[9] Gyongy I, 1996, PROBAB THEORY REL, V105, P143
[10] ON NONDEGENERATE QUASI-LINEAR STOCHASTIC PARTIAL-DIFFERENTIAL EQUATIONS
GYONGY, I
[J]. POTENTIAL ANALYSIS, 1995, 4 (02) : 157 - 171

← 1 2 3 →