Gradient estimate for OrnsteinUhlenbeck jump processes

摘要

By using absolutely continuous lower bounds of the Lvy measure, explicit gradient estimates are derived for the semigroup of the corresponding Lvy process with a linear drift. A derivative formula is presented for the conditional distribution of the process at time t under the condition that the process jumps before t. Finally, by using bounded perturbations of the Lvy measure, the resulting gradient estimates are extended to linear SDEs driven by Lvy-type processes.