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

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  • Bachmann, Stefan

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.

Suggested Citation

  • Bachmann, Stefan, 2020. "On the strong Feller property for stochastic delay differential equations with singular drift," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 4563-4592.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:8:p:4563-4592
    DOI: 10.1016/j.spa.2020.01.008
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    References listed on IDEAS

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    1. Blei, Stefan & Engelbert, Hans-Jürgen, 2013. "One-dimensional stochastic differential equations with generalized and singular drift," Stochastic Processes and their Applications, Elsevier, vol. 123(12), pages 4337-4372.
    2. Rutkowski, Marek, 1990. "Stochastic differential equations with singular drift," Statistics & Probability Letters, Elsevier, vol. 10(3), pages 225-229, August.
    3. Wang, Feng-Yu & Yuan, Chenggui, 2011. "Harnack inequalities for functional SDEs with multiplicative noise and applications," Stochastic Processes and their Applications, Elsevier, vol. 121(11), pages 2692-2710, November.
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