Strict positivity for stochastic heat equations

被引：20

作者：

Tessitore, G ^{[1
]}

Zabczyk, J

机构：

[1] Univ Florence, Dipartimento Matemat Appl, Florence, Italy

[2] Polish Acad Sci, Inst Math, Warsaw, Poland

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 1998年 / 77卷 / 01期

关键词：

heat equations; stochastic evolutions; positivity;

D O I：

10.1016/S0304-4149(98)00024-6

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：

The paper is concerned with the heat equation perturbed by a spatially homogeneous Wiener process. It is shown, under general conditions on the spectral density of the noise, that solutions starting from non-negative initial conditions are strictly positive for all positive times. The result has an application to the existence of a stationary solution to a stochastic Burgers equation in dimensions higher than 2. (C) 1998 Elsevier Science B.V. All rights reserved.

引用

页码：83 / 98

页数：16

共 15 条

[1] STOCHASTIC PARTIAL-DIFFERENTIAL EQUATIONS IN M-TYPE-2 BANACH-SPACES [J].

BRZEZNIAK, Z .

POTENTIAL ANALYSIS, 1995, 4 (01) :1-45

[2]

BRZEZNIAK Z, 1997, RANDOM EVOLUTIONS RD

[3]

Chow P.L., 1990, Stoch. Stoch. Rep., V29, P377, DOI DOI 10.1080/17442509008833622

[4]

Da Prato G, 1992, STOCHASTIC EQUATIONS

[5] SPATIALLY HOMOGENEOUS RANDOM EVOLUTIONS [J].

DAWSON, DA ;

SALEHI, H .

JOURNAL OF MULTIVARIATE ANALYSIS, 1980, 10 (02) :141-180

[6]

DETTWEILER E, 1985, STOCHASTIC INTEGRATI

[7]

KIFER Y, 1997, IN PRESS PROBAB THEO

[8]

MALGARINI LB, 1994, THESIS U ROMA TOR VE

[9]

Mueller C., 1991, Stochastics and Stochastics Reports, V37, P225, DOI 10.1080/17442509108833738

[10]

Pardoux E., 1975, Equations aux derivees partielles stochastiques non lineaires monotones

← 1 2 →