Ornstein-Uhlenbeck Equations with time-dependent coefficients and Levy Noise in finite and infinite dimensions

TL;DR

This paper addresses the analysis of Ornstein-Uhlenbeck equations with time-dependent coefficients driven by Levy noise in both finite and infinite dimensions, establishing existence, invariance, and functional inequalities.

Contribution

It provides a comprehensive solution framework for time-dependent linear SPDEs with Levy noise, including invariant measures and generator characterization.

Findings

Existence of generalized invariant measures

Characterization of the generator on L^2-space

Derivation of Poincare and Harnack inequalities

Abstract

We solve a time-dependent linear SPDE with additive Levy noise in the mild and weak sense. Existence of a generalized invariant measure for the associated transition semigroup is established and the generator is characterized on the corresponding L^2-space. The square field operator is calculated, allowing to derive a Poincare and a Harnack inequality.