Exponential Convergence for Semilinear SDEs Driven by L\'evy Processes on Hilbert Spaces

TL;DR

This paper establishes exponential convergence properties for semilinear stochastic differential equations driven by jump processes in Hilbert spaces, utilizing an integration by parts formula to analyze ergodicity and derivatives.

Contribution

It introduces a novel integration by parts formula for jump processes on Hilbert spaces and applies it to study ergodicity and derivative formulas for nonlinear SPDEs driven by jumps.

Findings

Derived an integration by parts formula for jump processes on Hilbert spaces.

Proved exponential ergodicity for certain nonlinear SPDEs driven by jump processes.

Analyzed derivative formulas for solutions to jump-driven SPDEs.

Abstract

In this paper, an integration by parts formula was derived for jump processes on Hilbert spaces. Using this formula, we investigated derivative formula and exponential ergodicity for nonlinear SPDEs driven by purely jump processes.