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Article Dans Une Revue Stochastic Processes and their Applications Année : 2021

WELL-POSEDNESS AND APPROXIMATION OF SOME ONE-DIMENSIONAL LÉVY-DRIVEN NON-LINEAR SDES

Résumé

In this article, we are interested in the strong well-posedness together with the numerical approximation of some one-dimensional stochastic differential equations with a non-linear drift, in the sense of McKean-Vlasov, driven by a spectrally-positive Lévy process and a Brownian motion. We provide criteria for the existence of strong solutions under non-Lipschitz conditions of Yamada-Watanabe type without non-degeneracy assumption. The strong convergence rate of the propagation of chaos for the associated particle system and of the corresponding Euler-Maruyama scheme are also investigated. In particular, the strong convergence rate of the Euler-Maruyama scheme exhibits an interplay between the regularity of the coefficients and the order of singularity of the Lévy measure around zero.
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Dates et versions

hal-02446337 , version 1 (20-01-2020)

Identifiants

Citer

Noufel Frikha, Libo Li. WELL-POSEDNESS AND APPROXIMATION OF SOME ONE-DIMENSIONAL LÉVY-DRIVEN NON-LINEAR SDES. Stochastic Processes and their Applications, 2021, 132, pp.76-107. ⟨10.1016/j.spa.2020.10.002⟩. ⟨hal-02446337⟩
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