Invariant cones for jump-diffusions in infinite dimensions

TL;DR

This paper establishes conditions under which certain convex cones remain invariant for jump-diffusion SPDEs in infinite-dimensional spaces, with applications in sciences and economics.

Contribution

It provides sufficient and necessary conditions for invariance of convex cones in jump-diffusion SPDEs, extending understanding in infinite-dimensional stochastic analysis.

Findings

Conditions for invariance of convex cones in jump-diffusion SPDEs

Application to positive cones in abstract L^2-spaces

Analysis of SPDEs in natural sciences and economics

Abstract

In this paper we provide sufficient conditions for stochastic invariance of closed convex cones for stochastic partial differential equations (SPDEs) of jump-diffusion type, and clarify when these conditions are necessary. Our results apply to the positive cone of abstract $L^2$-spaces. Furthermore, we present a series of applications, where we investigate SPDEs arising in natural sciences and economics.