The viability property of jump diffusion processes on Riemannian manifolds

TL;DR

This paper investigates the conditions under which jump diffusion processes remain within closed submanifolds of Euclidean space, providing necessary and sufficient criteria along with illustrative examples.

Contribution

It establishes a comprehensive criterion for the viability of jump diffusion processes on Riemannian manifolds, extending existing results to include jumps.

Findings

Derived necessary and sufficient conditions for viability.

Provided concrete examples illustrating the criteria.

Extended viability analysis to jump diffusion processes.

Abstract

In this note, we consider the necessary and sufficient condition for viability property of diffusion processes with jumps on closed submanifolds of $R^{m}$ with some concrete examples.