非线性随机泛函系统隐式方法的收敛率  

Strong Convergence Rate of Implicit Methods for Nonlinear Stochastic Functional Systems

作　　者：孟雪井[1] 周少波[2,3] MENG Xuejing;ZHOU Shaobo(School of Statistics and Mathematics,Hubei University of Economics,Wuhan 430205;School of Mathematics and Statistics,Huazhong University of Science and Technology,Wuhan 430074;Hubei Key Laboratory of Engineering Modeling and Scientific Computing,Huazhong University of Science and Technology,Wuhan 430074)

机构地区：[1]湖北经济学院统计与数学学院,武汉430205 [2]华中科技大学数学与统计学院,武汉430074 [3]华中科技大学工程建模与科学计算湖北省重点实验室,武汉430074

出　　处：《系统科学与数学》2025年第1期21-40,共20页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(12471279,12171173,12071031)资助课题。

摘　　要：文章研究了高阶非线性中立型随机泛函微分系统倒向欧拉算法具有近似于0.5阶的强收敛性.首先介绍了中立型随机泛函微分系统的离散和连续隐式欧拉格式,证明了精确解和近似解的一致有界性,并建立了一系列估计,在此基础上,证明了中立型随机泛函微分系统在Lp意义上的强收敛率,并运用计算机仿真验证所得的结论.This paper investigates the strong convergence with approximately 0.5 order for the backward Euler-Maruyama scheme for high-order nonlinear neutral stochastic functional differential systems.Firstly we propose the discrete and con-tinuous implicit Euler-Maruyama approximate forms for the neutral-type systems.Then,we show that the exact and approximate solutions are uniformly bounded.Secondly,we summarize a series of approximate estimations on the two kinds of so-lutions,which pave the way for proving the desired strong convergence rate for the neutral stochastic functional differential systems in the LP-sense.Finally,we provide numerical examples to illustrate the theoretical results.

关 键 词：强收敛率 矩有界 随机泛函微分系统 隐式欧拉方法 GRONWALL不等式 

分 类 号：O177[理学—数学]