Invariant cones for jump-diffusions in infinite dimensions

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.

46 pages

References in corpus (2)

• Stochastic mortality models: An infinite dimensional approach
• Invariance of closed convex cones for stochastic partial differential equations

Cited by in corpus (1)

• Linear estimators for Gaussian random variables in Hilbert spaces