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Particles Systems for mean reflected BSDEs
Stochastic Processes and their Applications ( IF 1.1 ) Pub Date : 2021-01-01 , DOI: 10.1016/j.spa.2020.09.010
Philippe Briand , Hélène Hibon

In this paper, we deal with Reflected Backward Stochastic Differential Equations for which the constraint is not on the paths of the solution but on its law as introduced by Briand, Elie and Hu in [3]. We extend the recent work [2] of Briand, Chaudru de Raynal, Guillin and Labart on the chaos propagation for mean reflected SDEs to the backward framework. When the driver does not depend on z, we are able to treat general reflexions for the particles system. We consider linear reflexion when the driver depends also on z. In both cases, we get the rate of convergence of the particles system towards the square integrable deterministic flat solution to the mean reflected BSDE.

中文翻译:

平均反射 BSDE 的粒子系统

在本文中,我们处理反射后向随机微分方程,其约束不是在解的路径上,而是在其定律上,如 Briand、Elie 和 Hu 在 [3] 中介绍的那样。我们将 Briand、Chaudru d​​e Raynal、Guillin 和 Labart 最近关于平均反射 SDE 混沌传播的工作 [2] 扩展到后向框架。当驱动程序不依赖于 z 时,我们能够处理粒子系统的一般反射。当驱动程序也依赖于 z 时,我们考虑线性反射。在这两种情况下,我们都得到了粒子系统向平均反射 BSDE 的平方可积确定性平坦解的收敛率。
更新日期:2021-01-01
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