Gradient Estimate for Ornstein-Uhlenbeck Jump Processes

Details Gradient Estimate for Ornstein-Uhlenbeck Jump Processes Gradient Estimate for Ornstein-Uhlenbeck Jump Processes

2010-05-27

arxiv.org/abs/1005.5023v3

Mathematics

Probability

17

Scientific paper

10.1016/j.spa.2010.12.002

By using absolutely continuous lower bounds of the L\'evy measure, explicit gradient estimates are derived for the semigroup of the corresponding L\'evy 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 L\'evy measure, the resulting gradient estimates are extended to linear SDEs driven by L\'evy-type processes.

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