Space-time continuous solutions to SPDE's driven by a homogeneous Wiener process

被引：73

作者：

Brzezniak, Z ^{[1
]}

Peszat, S

机构：

[1] Univ Hull, Dept Pure Math, Hull HU6 7RX, N Humberside, England

[2] Polish Acad Sci, Inst Math, PL-31027 Krakow, Poland

来源：

STUDIA MATHEMATICA | 1999年 / 137卷 / 03期

关键词：

stochastic partial differential equations in L-q-spaces; homogeneous Wiener process; random environment; stochastic integration in Banach spaces;

D O I：

10.4064/sm-137-3-261-299

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Stochastic partial differential equations on R-d are considered. The noise is supposed to be a spatially homogeneous Wiener process. Using the theory of stochastic integration in Banach spaces we show the existence of a Markovian solution in a certain weighted L-q-space. Then we obtain the existence of a space continuous solution by means of the Da Prate, Kwapien and Zabczyk factorization identity for stochastic convolutions.

引用

页码：261 / 299

页数：39

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