On the Strong Feller Property of Stochastic Delay Differential Equations with Singular Drift

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. 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.

References in corpus (4)

• Pathwise uniqueness and continuous dependence for SDEs with nonregular drift
• Group-valued continuous functions with the topology of pointwise convergence
• One-dimensional Stochastic Differential Equations with Generalized and Singular Drift
• Well-Posedness and Stability for a Class of Stochastic Delay Differential Equations with Singular Drift

Cited by in corpus (1)

• On the Strong Feller Property and Well-Posedness for SDEs with Functional, Locally Unbounded Drift