On the strong Feller property for stochastic delay differential equations with singular drift

Stefan Bachmann

Stochastic Processes and their Applications, 2020, vol. 130, issue 8, 4563-4592

Abstract: In this paper, we prove the strong Feller property for stochastic delay (or functional) differential equations with singular drift. We extend an approach of Maslowski and Seidler to derive the strong Feller property of those equations, see Maslowski and Seidler (2000). The argumentation is based on the well-posedness and the strong Feller property of the equations’ drift-free version. To this aim, we investigate a certain convergence of random variables in topological spaces in order to deal with discontinuous drift coefficients.

Keywords: Stochastic delay differential equations; Stochastic functional differential equation; Strong feller property; Singular drift; Zvonkin’s transformation (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2020.01.008

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