Theory of Probability &Its Applications, Volume 65, Issue 1, Page 82-101, January 2020.
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 by H. Kunita [Stochastic differential equations based on Lévy processes and stochastic flows of diffeomorphisms, in Real and Stochastic Analysis, Birkhäuser Boston, 2004, pp. 305--373] for first order differentiability and rely on the Burkholder--Davis--Gundy (BDG) inequality for time inhomogeneous Poisson random measures on $R_+\times R$, for which we provide a new proof.

中文翻译：

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带跳的随机微分方程流的可积性和正则性

概率论及其应用，第65卷，第1期，第82-101页，2020年1月。
我们为带跳的随机微分方程组的所有阶求微分导出了充分的条件，并证明了相关的$ L ^ p $-可积性结果对于所有订单。我们的结果扩展了H. Kunita [基于Lévy过程和微分形的随机流的随机微分方程，在真实和随机分析，BirkhäuserBoston，2004，第305--373页]中获得的一阶可微性，并依赖于时间非均匀泊松随机测度在$ R _ + \ R $上的Burkholder-Davis-Gundy（BDG）不等式，为此我们提供了新的证明。