Estimates of gradient perturbation series

TL;DR

This paper provides bounds for the series expansion of transition densities under additive gradient perturbations, offering insights into their behavior under specific integrability conditions.

Contribution

It introduces new upper and lower bounds for gradient perturbation series of transition densities under certain conditions.

Findings

Established bounds for perturbation series

Applicable to additive gradient perturbations

Enhanced understanding of transition density behavior

Abstract

We give upper and lower bounds of perturbation series for transition densities, corresponding to additive gradient perturbations satisfying certain space-time integrability conditions.