论文标题
核空间的随机卷积和随机演化方程的时间规律性
Time regularity of stochastic convolutions and stochastic evolution equations in duals of nuclear spaces
论文作者
论文摘要
令$φ$ a本地凸出空间和$ψ$是一个准完整的，出生的，核空间（例如平滑功能和分布的空间）$φ'$和$ψ'$。在这项工作中，我们介绍了足够的条件，以适应$ψ'$的时间规律性属性 - 有价值的随机卷积$ \ int_ {0}^{t} {t} \ int_ {u} s（t-r）在$ψ$上，$ r（r，ω，u）$是合适的操作员表格$φ'$ to $ψ'$，$ m $是$φ'$上的圆柱式估价尺寸。我们的结果是将后者应用于研究$ψ'$的随机演变方程的解决方案的时间规律性。
Let $Φ$ a locally convex space and $Ψ$ be a quasi-complete, bornological, nuclear space (like spaces of smooth functions and distributions) with dual spaces $Φ'$ and $Ψ'$. In this work we introduce sufficient conditions for time regularity properties of the $Ψ'$-valued stochastic convolution $\int_{0}^{t} \int_{U} S(t-r)'R(r,u) M(dr,du)$, $t \in [0,T]$, where $(S(t): t \geq 0)$ is a $C_{0}$-semigroup on $Ψ$, $R(r,ω,u)$ is a suitable operator form $Φ'$ into $Ψ'$ and $M$ is a cylindrical-martingale valued measure on $Φ'$. Our result is latter applied to study time regularity of solutions to $Ψ'$-valued stochastic evolutions equations.
