On the Estimates of the Density of the Purely Discontinuous Girsanov Transforms of $α$-Stable-like Processes

Abstract

In this paper, we study the purely discontinuous Girsanov transforms which were discussed in Chen and Song \cite{CS2} and Song \cite{S3}. We show that the transition density of any purely discontinuous Girsanov transform of a $α$-stable-like process, which can be nonsymmetric, is comparable to the transition density of the $α$-stable-like process.