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

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In this paper, we study the purely discontinuous Girsanov transforms which were discussed in Chen and Song CS2 and Song 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.