Split-step balanced θ-method for SDEs with non-globally Lipschitz continuous coefficients

被引：12

作者：

Liu, Yufen ^{[1
]}

Cao, Wanrong ^{[1
]}

Li, Yuelin ^{[2
]}

机构：

[1] Southeast Univ, Sch Math, Nanjing 210096, Peoples R China

[2] Columbia Univ, Inst Social & Econ Res & Policy, New York, NY 10027 USA

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2022年 / 413卷

关键词：

Nonlinear problems; The balanced method; Strong convergence; Exponential stability; Mean-square contraction; STOCHASTIC DIFFERENTIAL-EQUATIONS; SURE EXPONENTIAL STABILITY; EULER-MARUYAMA METHOD; STRONG-CONVERGENCE; MEAN-SQUARE; NUMERICAL-SOLUTION; MILSTEIN SCHEMES; IMPLICIT; DIVERGENCE; JUMPS;

D O I：

10.1016/j.amc.2021.126437

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a split-step balanced theta-method (SSBT) has been presented for solving stochastic differential equations (SDEs) under non-global Lipschitz conditions, where theta is an element of[0, 1] is a parameter of the scheme. The moment boundedness and strong convergence of the numerical solution have been studied, and the convergence rate is 0.5. Moreover, under some conditions it is proved that the SSBT scheme can preserve the exponential mean-square stability of the exact solution when theta is an element of(1/2, 1] for every step size h > 0. Numerical examples verify the theoretical findings. (C) 2021 Elsevier Inc. All rights reserved.

引用

页数：15

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