In this work, we consider the Hölder continuous regularity of stochastic convolutions for a class of linear stochastic retarded functional differential equations with distributed delay in Hilbert spaces. By focusing on distributed delays, we first establish some more delicate estimates for fundamental solutions than those given in Liu (Discrete Contin. Dyn. Syst. Ser. B 25(4), 1279–1298, 2020). Then we apply these estimates to stochastic convolutions incurred by distributed delay to study their regularity property. Last, we present some easily-verified results by considering the regularity of a class of systems whose delay operators have the same order derivatives as those in instantaneous ones.

在这项工作中，我们考虑了希尔伯特空间中具有分布时滞的一类线性随机滞后泛函微分方程的随机卷积的Hölder连续正则性。通过关注分布式延迟，我们首先建立了一些基本解决方案的估计，而不是Liu中给出的估计（Discrete Contin。Dyn。Syst。Ser。B 25（4），1279-1298，2020）。然后我们将这些估计值应用于由分布延迟引起的随机卷积，以研究其正则性。最后，我们通过考虑一类延迟算子与瞬时算子具有相同阶导数的系统的正则性，给出一些容易验证的结果。