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

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

2006-11-19

arxiv.org/abs/math/0611566v1

Mathematics

Probability

33 pages

Scientific paper

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
$\alpha$-stable-like process, which can be nonsymmetric, is comparable to the
transition density of the $\alpha$-stable-like process.

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