Convergence of hitting times for jump-diffusion processes

TL;DR

This paper studies how the hitting times of jump-diffusion processes converge when the underlying stochastic differential equations with jumps are approximated, providing theoretical guarantees under certain assumptions.

Contribution

It establishes the convergence of solutions and hitting times for a sequence of jump-diffusion SDEs under reasonable conditions, advancing understanding of their asymptotic behavior.

Findings

Solutions to jump-diffusion SDEs converge under specified assumptions.

Hitting times of the processes also converge as the equations approximate each other.

Provides theoretical foundation for analyzing jump-diffusion hitting times.

Abstract

We investigate the convergence of hitting times for jump-diffusion processes. Specifically, we study a sequence of stochastic differential equations with jumps. Under reasonable assumptions, we establish the convergence of solutions to the equations and of the moments when the solutions hit certain sets.