Coupling and Strong Feller for Jump Processes on Banach Spaces

Abstract

By using lower bound conditions of the Lévy measure w.r.t. a nice reference measure, the coupling and strong Feller properties are investigated for the Markov semigroup associated with a class of linear SDEs driven by (non-cylindrical) Lévy processes on a Banach space. Unlike in the finite-dimensional case where these properties have also been confirmed for Lévy processes without drift, in the infinite-dimensional setting the appearance of a drift term is essential to ensure the quasi-invariance of the process by shifting the initial data. Gradient estimates and exponential convergence are also investigated. The main results are illustrated by specific models on the Wiener space and separable Hilbert spaces.

31 pages

References in corpus (7)

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Cited by in corpus (3)

• Gradient Estimate for Ornstein-Uhlenbeck Jump Processes
• Exponential Convergence for Semilinear SDEs Driven by Lévy Processes on Hilbert Spaces
• Linear Evolution Equations with Cylindrical Lévy Noise: Gradient Estimates and Exponential Ergodicity