Stochastic continuity, irreducibility and non confluence for SDEs with jumps

TL;DR

This paper studies key properties of solutions to jump-diffusion stochastic differential equations, introducing weaker conditions than previous work, and provides an example to validate these new criteria.

Contribution

It presents novel, less restrictive conditions for stochastic continuity, irreducibility, and non confluence in SDEs with jumps, expanding theoretical understanding.

Findings

Established weaker conditions for stochastic continuity

Proved irreducibility and non confluence under new criteria

Provided an example supporting the new conditions

Abstract

In this paper, we investigate stochastic continuity (with respect to the initial value), irreducibility and non confluence property of the solutions of stochastic differential equations with jumps. The conditions we posed are weaker than those relevant conditions existing in the literature. We also provide an example to support our new conditions.