Gradient Estimate for Ornstein-Uhlenbeck Jump Processes

Feng-Yu Wang

doi:10.1016/j.spa.2010.12.002

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arXiv · 1005.5023

Gradient Estimate for Ornstein-Uhlenbeck Jump Processes

Feng-Yu Wang

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Abstract

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

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Feng-Yu Wang. 2010-09-23. Gradient Estimate for Ornstein-Uhlenbeck Jump Processes. https://doi.org/10.1016/j.spa.2010.12.002

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