Total variation distance between a jump-equation and its Gaussian approximation

Vlad Bally, Yifeng Qin

Published 2021-09-23Version 1

We deal with the stochastic di erential equations with jumps. We replace the "small jumps" by a Brownian motion to make an approximation. In this paper, we prove that the approximation process converges to the original process in total variation distance. Moreover, we also give an estimate of the distance between the densities of the two processes. These are done by some integration by parts techniques in Malliavin calculus.