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

共 50 条

[21] On the estimation of backward stochastic differential equations
B. I. Ananyev
Proceedings of the Steklov Institute of Mathematics, 2016, 292 : 14 - 26
[22] A property of backward stochastic differential equations
Chen, ZJ
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1998, 326 (04): : 483 - 488
[23] On the Estimation of Backward Stochastic Differential Equations
Ananyev, B. I.
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2016, 292 : S14 - S26
[24] ANTICIPATED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS
Peng, Shige
Yang, Zhe
ANNALS OF PROBABILITY, 2009, 37 (03): : 877 - 902
[25] Backward stochastic differential equations in the plane
Zaïdi N.L.
Nualart D.
Potential Analysis, 2002, 16 (4) : 373 - 386
[26] SWITCHING GAME OF BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND ASSOCIATED SYSTEM OF OBLIQUELY REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS
Hu, Ying
Tang, Shanjian
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2015, 35 (11) : 5447 - 5465
[27] The comparison of the convergence speed between Picard, Mann, Krasnoselskij and Ishikawa iterations in Banach spaces
Xue, Zhiqun
FIXED POINT THEORY AND APPLICATIONS, 2008,
[28] ANDERSON-ACCELERATED CONVERGENCE OF PICARD ITERATIONS FOR INCOMPRESSIBLE NAVIER-STOKES EQUATIONS
Pollock, Sara
Rebholz, Leo G.
Xia, Mengying
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2019, 57 (02) : 615 - 637
[29] MEAN-SQUARE CONVERGENCE OF NUMERICAL APPROXIMATIONS FOR A CLASS OF BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS
Chen, Chuchu
Hong, Jialin
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2013, 18 (08): : 2051 - 2067
[30] Rate of convergence of an empirical regression method for solving generalized backward stochastic differential equations
Lemor, Jean-Philippe
Gobet, Emmanuel
Warin, Xavier
BERNOULLI, 2006, 12 (05) : 889 - 916

← 1 2 3 4 5 →