Well-posedness and approximation of some one-dimensional L\'evy-driven non-linear SDEs

Autor:	Frikha, Noufel, Li, Libo
Rok vydání:	2020
Předmět:	Mathematics - Probability
Druh dokumentu:	Working Paper
Popis:	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 L{\'e}vy 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 L{\'e}vy measure around zero. Comment: 24p
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2001.07505 Zobrazit plný text záznamu View this record from Arxiv