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.
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页码：261 / 299
页数：39
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