Invariant manifolds with boundary for jump-diffusions

TL;DR

This paper establishes conditions under which finite-dimensional submanifolds with boundary remain invariant in Hilbert spaces for SPDEs driven by Wiener processes and Poisson measures, advancing understanding of stochastic invariance.

Contribution

It provides necessary and sufficient criteria for stochastic invariance of manifolds with boundary in the context of jump-diffusions in Hilbert spaces.

Findings

Derived conditions for invariance of manifolds with boundary

Applied results to stochastic partial differential equations

Enhanced understanding of boundary behavior in jump-diffusions

Abstract

We provide necessary and sufficient conditions for stochastic invariance of finite dimensional submanifolds with boundary in Hilbert spaces for stochastic partial differential equations driven by Wiener processes and Poisson random measures.