Stability of densities for perturbed degenerate Diffusions

TL;DR

This paper investigates how small changes in the coefficients of certain degenerate diffusion processes influence their probability densities, providing precise quantifications under specific assumptions with applications across finance and kinetic modeling.

Contribution

It offers new quantitative estimates on the sensitivity of densities for Kolmogorov-like degenerate diffusions to coefficient perturbations, under sharp assumptions.

Findings

Quantitative bounds on density sensitivity to coefficient perturbations

Applicability to mathematical finance models

Relevance to kinetic process analysis

Abstract

We study the sensitivity of the densities of some Kolmogorov like degenerate diffusion processes with respect to a perturbation of the coefficients of the non-degenerate component. Under suitable (quite sharp) assumptions we quantify how the pertubation of the SDE affects the density. Natural applications of these results appear in various fields from mathematical finance to kinetic models.