Integrability and regularity of the flow of stochastic differential equations with jumps

Abstract

We derive sufficient conditions for the differentiability of all orders for the flow of stochastic differential equations with jumps, and prove related $L^p$-integrability results for all orders. Our results extend similar results obtained in [Kun04] for first order differentiability and rely on the Burkholder-Davis-Gundy inequality for time inhomogeneous Poisson random measures on ${\mathbb{R}}_{+}\times \mathbb{R}$, for which we provide a new proof.