Gradient Estimate for Ornstein-Uhlenbeck Jump Processes

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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Cited by in corpus (3)

• Exponential ergodicity and regularity for equations with Lévy noise
• Constructions of Coupling Processes for Lévy Processes
• On the Coupling Property and the Liouville Theorem for Ornstein-Uhlenbeck Processes