论文标题
良好的一维lévy驱动的非线性SDE的适应性和近似
Well-posedness and approximation of some one-dimensional Lévy-driven non-linear SDEs
论文作者
论文摘要
在本文中，我们对强大的良好性感兴趣，以及一些一维随机微分方程的数值近似，从麦基恩·维拉索夫（McKean-Vlasov）的意义上讲，由频谱阳性的l {é} vy过程和布朗运动和布朗运动驱动。我们提供了在Yamada-Watanabe类型的非黎甲曲条件下存在强溶液的标准。还研究了相关粒子系统和相应的Euler-Maruyama方案的混乱传播的强收敛速率。特别是，Euler-Maruyama方案的强收敛速率在系数的规律性与L {é} vy的奇异性范围之间表现出相互作用。
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{é}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{é}vy measure around zero.
