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

Jean-Christophe Breton; Nicolas Privault

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arXiv · 1902.03542

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

Jean-Christophe Breton·Nicolas Privault

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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 ${\Bbb R}_+\times {\Bbb R}$, for which we provide a new proof.

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Jean-Christophe Breton, Nicolas Privault. 2019-02-10. Integrability and regularity of the flow of stochastic differential equations with jumps. https://arxiv.org/abs/1902.03542

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