Linear Evolution Equations with Cylindrical Lévy Noise: Gradient Estimates and Exponential Ergodicity

Abstract

Explicit coupling property and gradient estimates are investigated for the linear evolution equations on Hilbert spaces driven by an additive cylindrical Lévy process. The results are efficiently applied to establish the exponential ergodicity for the associated transition semigroups. In particular, our results extend recent developments on related topic for cylindrical symmetric $\alpha$-stable processes.

References in corpus (3)

• Gradient Estimate for Ornstein-Uhlenbeck Jump Processes
• On linear evolution equations with cylindrical Lévy noise
• Exponential ergodicity of semilinear equations driven by Lévy processes in Hilbert spaces