Strong Feller property for SDEs driven by multiplicative cylindrical stable noise

Tadeusz Kulczycki, Michał Ryznar, Paweł Sztonyk

We consider the stochastic differential equation $d{X}_t=A(X_{t-})d{Z}_t$, $X_0=x$, driven by cylindrical $\alpha$-stable process $Z_t$ in $R^d$, where $\alpha \in (0,1)$ and $d\ge 2$.…