Exponential mixing for SPDEs driven by highly degenerate L\'evy noises

TL;DR

This paper proves exponential mixing for a class of SPDEs driven by highly degenerate pure jump Le9vy noises, including -stable processes, using a coupling method.

Contribution

It introduces a novel coupling approach to establish exponential mixing for SPDEs with highly degenerate Le9vy noises, expanding understanding of their long-term behavior.

Findings

SPDEs driven by degenerate Le9vy noises exhibit exponential mixing.

The coupling method effectively handles highly degenerate jump noises.

Results include -stable processes with  in (0,2).

Abstract

By a coupling method, we prove that a family of stochastic partial differential equations (SPDEs) driven by highly degenerate pure jump L\'evy noises are exponential mixing. These pure jump L\'evy noises include $\alpha$-stable process with $\alpha \in (0,2)$