Density stability for some L\'evy-driven Stochastic Differential Equations

TL;DR

This paper investigates how perturbations in coefficients of Le9vy-driven stochastic differential equations affect the solution's density, extending Gaussian noise results to stable noise cases.

Contribution

It provides a quantitative analysis of density stability for SDEs driven by tempered stable Le9vy processes, generalizing previous Gaussian noise findings.

Findings

Density differences are bounded by coefficient proximity.

Results extend Gaussian noise stability to stable noise cases.

Quantitative bounds on density perturbations are established.

Abstract

We consider a Stochastic Differential Equation driven by a L\'evy process whose L\'evy measure satisfy a tempered stable domination. We study how a perturbation of the coefficients reflects on the density of the solution. We quantify the distance between the densities in term of the proximity of the coefficients. This extend to the stable case the works of [KKM15], where the noise is Gaussian.