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Article Dans Une Revue Theory of Probability and Its Applications c/c of Teoriia Veroiatnostei i Ee Primenenie Année : 2020

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

Résumé

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.

Dates et versions

hal-02405866 , version 1 (11-12-2019)

Identifiants

Citer

Jean-Christophe Breton, Nicolas Privault. Integrability and regularity of the flow of stochastic differential equations with jumps. Theory of Probability and Its Applications c/c of Teoriia Veroiatnostei i Ee Primenenie, 2020, 65 (1), pp.82-101. ⟨10.1137/S0040585X97T989830⟩. ⟨hal-02405866⟩
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