Convergence of numerical solutions to stochastic differential equations with Markovian switching

被引：3

作者：

Fan, Zhencheng ^{[1
]}

机构：

[1] Minjiang Univ, Inst Math, Fuzhou 350108, Fujian, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2017年 / 315卷

关键词：

Stochastic differential equations; Markovian switching; Generalized Ito formula; Simulation; Numerical approximations; DELAY EQUATIONS; EXPONENTIAL STABILITY; POISSON JUMP; APPROXIMATIONS; SDDES;

D O I：

10.1016/j.amc.2017.07.061

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The paper develops strong approximation schemes for solutions of stochastic differential equations with Markovian switching (SDEwMSs). The convergent orders of existing strong numerical schemes all are 0.5. This paper provides a convergence theorem for the construction of strong approximations of any given order of convergence for SDEwMS5, and then constructs the order 1 scheme, the order 1.5 scheme. The paper also develops a new way to simulate the Markov chain and hence the order 1 scheme. Finally, a numerical example is provided to illustrate the theoretical results. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：176 / 187

页数：12

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