一类NSFDE的带随机步长EM 数值解的渐近性质

马瑞楠; 马丽*

文章摘要

马瑞楠，马丽*.一类NSFDE的带随机步长EM 数值解的渐近性质[J].海南师范大学学报自科版,2018,31(3):295-305

一类NSFDE的带随机步长EM 数值解的渐近性质

Asymptotic Properties of Euler - Maruyama Solution Carrying Stochastic Stepsize for NSFDE

DOI：10.12051/j.issn.1674-4942.2018.03.009

中文关键词: 中立随机泛函微分方程带随机步长的EM 逼近非负半鞅收敛定理几乎处处稳定

英文关键词: neutral stochastic functional differential equations Euler - Maruyama method with stochastic variable step⁃ size nonnegative semimartingale convergence theorem almost sure stability

基金项目:海南省科研创新资助项目（Hsyx2017-27）；国家自然科学基金项目（11861029）

作者	单位
马瑞楠，马丽*	海南师范大学数学与统计学院，海南海口571158）

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中文摘要:

研究了一类有中立项的随机泛函微分方程的EM 逼近，给出了带随机步长的EM 算法。由非负半鞅收敛定理证明了随机步长的EM 数值解几乎处处收敛到零。

英文摘要:

This study aimed to investigate the Euler - Maruyama(EM)approximation of a class of stochastic functional differential equations carrying neutral terms. The EM algorithm carrying stochastic stepsizes was also provided. By nonneg⁃ ative semimartingale convergence theorem, it was proved that the EM solution carrying stochastic stepsizes converged to zero almost surely.

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