Zhao Dong, Xuhui Peng, Yulin Song, Xicheng Zhang
Published 2013-12-28, updated 2014-02-15Version 2
Under full H\"ormander's conditions, we prove the strong Feller property of the semigroup determined by an SDE driven by additive subordinate Brownian motion, where the drift is allowed to be arbitrarily growth. For this, we extend a criterion due to Malicet-Poly \cite{Ma-Po} and Bally-Caramellino \cite{Ba-Ca} about the convergence of the laws of Wiener functionals in total variations. Moreover, the example of a chain of coupled oscillators is verified.
Comments: 10pages, Theorem 1.1 is improved
On the Strong Feller Property and Well-Posedness for SDEs with Functional, Locally Unbounded Drift
On the Strong Feller Property of Stochastic Delay Differential Equations with Singular Drift
On weak uniqueness for some degenerate SDEs by global $L^p$ estimates
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