Space-time continuous solutions to SPDE's driven by a homogeneous Wiener process
Space-time continuous solutions to SPDE's driven by a homogeneous Wiener process
复制标题
DOI：
10.4064/sm-137-3-261-299
复制
发表时间：
1999-01-01
影响因子：
0.8
通讯作者：
Peszat, S
中科院分区：
文献类型：
--
作者：
Brzezniak, Z;Peszat, S
考虑了R-d上的随机偏微分方程。假设噪声是空间均匀的Wiener过程。利用Banach空间中的随机积分理论，我们证明了在某个加权L-q-空间中马氏解的存在性。然后利用随机卷积的Da Prate，Kwapien和Zabczyk分解恒等式得到了空间连续解的存在性.
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.