This article is cited in 5 papers

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

J.-Ch. Breton^a, N. Privault<sup>b

a</sup> Université de Rennes, CNRS, IRMAR--UMR 6625, F-35000 Rennes, France
^b School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore

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 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.

Received: 04.02.2019
Revised: 10.10.2019
Accepted: 17.10.2019

DOI: 10.4213/tvp5291

 English version: Theory of Probability and its Applications, 2020, 65:1, 82–101

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