Density stability for some Lévy-driven Stochastic Differential Equations

Abstract

We consider a Stochastic Differential Equation driven by a Lévy process whose Lévy 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.