Maximal inequalities and space-time regularity of stochastic convolutions
Maximal inequalities and space-time regularity of stochastic convolutions
复制标题
随机卷积的最大不等式和时空规律性
DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
Jan Seidler
中科院分区：
文献类型：
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作者：
S. Peszat;Jan Seidler
随机卷积积分的时空正则性
J = {int^cdot_0 S（cdot-r）Z（r）W（r）}
在有界区域上的L^2 $-空间中研究了由圆柱Wiener过程$W$驱动的.假设半群S由2 m阶抛物边值问题的绿色函数给出，Z是一个乘法算子.在相当一般的假设下，证明了$J$在时间和空间上是保持器连续的.该方法也给出了连续函数空间中随机卷积的极大不等式。
Space-time regularity of stochastic convolution integrals
J = {int^cdot_0 S(cdot-r)Z(r)W(r)}
driven by a cylindrical Wiener process $W$ in an $L^2$-space on a bounded domain is investigated. The semigroup $S$ is supposed to be given by the Green function of a $2m$-th order parabolic boundary value problem, and $Z$ is a multiplication operator. Under fairly general assumptions, $J$ is proved to be Holder continuous in time and space. The method yields maximal inequalities for stochastic convolutions in the space of continuous functions as well.