Coupling and strong Feller for jump processes on Banach spaces (Q1947595)

The authors discuss properties of linear stochastic differential equations driven by purely jump non-cylindrical Levy process on a Banach space endowed with a reference measure quasi-invariant under a reasonable class of shift transforms. The Markov semigroup related to this class of equations is investigated in the context of regularity properties including the coupling and Feller properties, gradient estimates and exponential convergence. Because of the infinite-dimensional setting a drift part is necessary to derive the considered properties. Theoretical results are illustrated by two simple examples in which the reference measure is assumed to be the Wiener measure on the Brownian path space and the Gaussian measure on a separable Hilbert space, respectively.