A class of L\'evy driven SDEs and their explicit invariant measures

TL;DR

This paper identifies explicit invariant measures for a class of Le9vy-driven SDEs in finite and infinite dimensions, providing a unified explicit form and extending the results to Hilbert space settings.

Contribution

It introduces a class of SDEs with explicit invariant measures, applicable in both finite and infinite dimensions, including Hilbert spaces.

Findings

Explicit invariant measures for certain Le9vy-driven SDEs are derived.

The invariant measures are given in explicit form across all dimensions.

Extension of finite-dimensional results to infinite-dimensional Hilbert space SDEs.

Abstract

We describe a class of explicit invariant measures for both finite and infinite dimensional Stochastic Differential Equations (SDE) driven by L\'evy noise. We first discuss in details the finite dimensional case with a linear, resp. non linear, drift. In particular, we exhibit a class of such SDEs for which the invariant measures are given in explicit form, coherently in all dimensions. We then indicate how to relate them to invariant measures for SDEs on separable Hilbert spaces.