一类漂移系数分段连续的随机微分方程驯服Euler方法的Lp收敛率
Lp-convergence Rate of the Tamed Euler Scheme for SDEs with Piecewise Continuous Drift Coefficient
胡慧敏 1甘四清1
作者信息
- 1. 中南大学数学与统计学院,分析数学及其应用湖南省重点实验室,长沙,410083
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摘要
本文研究一类漂移系数分段连续的标量随机微分方程的驯服Euler方法的Lp收敛率.更确切地说,本文在漂移系数是分段连续的并且呈多项式增长,扩散系数是Lipschitz连续的并且在漂移系数的间断点处不为0的假设下,证明方程具有唯一的强解,并且对于任意的p∈[1,∞),驯服Euler方法的Lp收敛阶都可以达到1/2.此外,本文还提供一个数值算例来验证理论结果.
Abstract
In this paper we study the Lp-convergence rate of the tamed Euler scheme for scalar stochastic differential equations(SDEs)with piecewise continuous drift coefficient.More precisely,under the assumptions that the drift coefficient is piecewise continuous and polynomially growing and that the diffusion coefficient is Lipschitz continuous and non-zero at the discontinuity points of the drift coefficient,we show that the SDE has a unique strong solution and the Lp-convergence order of the tamed Euler scheme is at least 1/2 for all p ∈[1,∞).Moreover,a numerical example is provided to support our conclusion.
关键词
随机微分方程/漂移系数/驯服Euler方法/Lp收敛率Key words
Stochastic differential equation/Drift coefficient/Tamed Euler scheme/Lp-convergence rate引用本文复制引用
基金项目
National Natural Science Foundation of China(12371417)
National Natural Science Foundation of China(11971488)
出版年
2024
NETL
NSTL
万方数据