Stability properties of some port-Hamiltonian SPDEs

TL;DR

This paper investigates the existence, uniqueness, and exponential convergence of invariant measures for a class of stochastic partial differential equations, including stochastic port-Hamiltonian equations, with Gaussian and Poissonian noise.

Contribution

It establishes stability properties and invariant measure results for stochastic port-Hamiltonian PDEs with mixed noise types.

Findings

Proves existence and uniqueness of invariant measures.

Demonstrates exponential convergence to invariant measures.

Includes stochastic port-Hamiltonian equations as a special case.

Abstract

We examine the existence and uniqueness of invariant measures of a class of stochastic partial differential equations with Gaussian and Poissonian noise and its exponential convergence. This class especially includes a case of stochastic port-Hamiltonian equations.