Exponential mixing for SDEs forced by degenerate Levy noises

Abstract

We modify the coupling method established in [22, 20] and develop a technique to prove the exponential mixing of a 2D stochastic system forced by degenerate Levy noises. In particular, these Levy noises include $\alpha$-stable noises (0 < $\alpha$ < 2). Thanks to the stimulating discussion [14], this technique is promising to study the exponential mixing problem of SPDEs driven by degenerate symmetric $\alpha$-stable noises.

Some small errors in the proof of Theorem 2.4 were corrected

References in corpus (5)

• Densities for Ornstein-Uhlenbeck processes with jumps
• Gradient Estimate for Ornstein-Uhlenbeck Jump Processes
• Derivative formula and gradient estimate for SDEs driven by $\alpha$-stable processes
• On linear evolution equations with cylindrical Lévy noise
• Structural properties of semilinear SPDEs driven by cylindrical stable processes

Cited by in corpus (1)

• Exponential mixing for SPDEs driven by highly degenerate Lévy noises