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Some regularity results on stochastic convolutions in point delay differential equations perturbed by noise

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  • Liu, Kai

Abstract

In this work, we obtain some regularity results on stochastic convolutions for a class of abstract linear stochastic retarded functional differential equations with unbounded coefficient operators driven by white noise. We first establish some estimates on fundamental solutions which play an important role in the subsequent theory. Then we apply these estimates to some stochastic convolutions arising in stochastic delay differential equations to obtain the desired regularity property.

Suggested Citation

  • Liu, Kai, 2020. "Some regularity results on stochastic convolutions in point delay differential equations perturbed by noise," Statistics & Probability Letters, Elsevier, vol. 156(C).
    • Handle: RePEc:eee:stapro:v:156:y:2020:i:c:s0167715219302706
    DOI: 10.1016/j.spl.2019.108624
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