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Integrability and regularity of the flow of stochastic differential equations with jumps
Teoriâ veroâtnostej i ee primeneniâ, Tome 65 (2020) no. 1, pp. 103-125 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $\mathbf{R}_+\times \mathbf{R}$, for which we provide a new proof.
Keywords: stochastic differential equations with jumps, moment bounds, Poisson random measures, stochastic flows, Markov semigroups. 
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J.-Ch. Breton; N. Privault. Integrability and regularity of the flow of stochastic differential equations with jumps. Teoriâ veroâtnostej i ee primeneniâ, Tome 65 (2020) no. 1, pp. 103-125. http://geodesic.mathdoc.fr/item/TVP_2020_65_1_a5/

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