{"title":"Numerical solutions of stochastic functional differential equations with impulsive perturbations and Markovian switching","authors":"Ky Q. Tran , George Yin","doi":"10.1016/j.nahs.2023.101409","DOIUrl":null,"url":null,"abstract":"<div><p><span>This paper is focused on analysis of Euler–Maruyama-type approximations for stochastic functional differential equations with impulsive perturbations and Markovian switching. The motivation stems from a wide range of applications. The paper establishes mean square convergence of the approximations under a local </span>Lipschitz condition<span> and a linear growth condition. In addition, this work ascertains the rates of convergence of the numerical solutions under the global Lipschitz condition. Finally, the performance of the algorithm is demonstrated through a numerical example.</span></p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":null,"pages":null},"PeriodicalIF":3.7000,"publicationDate":"2023-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis-Hybrid Systems","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1751570X23000808","RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
This paper is focused on analysis of Euler–Maruyama-type approximations for stochastic functional differential equations with impulsive perturbations and Markovian switching. The motivation stems from a wide range of applications. The paper establishes mean square convergence of the approximations under a local Lipschitz condition and a linear growth condition. In addition, this work ascertains the rates of convergence of the numerical solutions under the global Lipschitz condition. Finally, the performance of the algorithm is demonstrated through a numerical example.
期刊介绍:
Nonlinear Analysis: Hybrid Systems welcomes all important research and expository papers in any discipline. Papers that are principally concerned with the theory of hybrid systems should contain significant results indicating relevant applications. Papers that emphasize applications should consist of important real world models and illuminating techniques. Papers that interrelate various aspects of hybrid systems will be most welcome.