On the speed of convergence of Picard iterations of backward stochastic differential equations

被引：0

作者：

Martin Hutzenthaler ^{[1
]}

Thomas Kruse ^{[2
]}

Tuan Anh Nguyen ^{[1
]}

机构：

[1] Faculty of Mathematics,University of Duisburg-Essen

[2] Institute of Mathematics,University of

来源：

Probability,Uncertainty and Quantitative Risk | 2022年 / 02期

关键词：

D O I：

暂无

中图分类号：

O211.63 [随机微分方程];

学科分类号：

摘要：

It is a well-established fact in the scientific literature that Picard iterations of backward stochastic differential equations with globally Lipschitz continuous nonlinearities converge at least exponentially fast to the solution.In this paper we prove that this convergence is in fact at least square-root factorially fast.We show for one example that no higher convergence speed is possible in general.Moreover,if the nonlinearity is zindependent,then the convergence is even factorially fast.Thus we reveal a phase transition in the speed of convergence of Picard iterations of backward stochastic differential equations.

引用

页码：133 / 150

页数：18

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