{"title":"The truncated Euler–Maruyama method of one-dimensional stochastic differential equations involving the local time at point zero","authors":"Kamal Hiderah","doi":"10.1515/rose-2023-2003","DOIUrl":null,"url":null,"abstract":"Abstract Recently, Mao developed a new explicit method, called the truncated Euler–Maruyama method for nonlinear SDEs, and established the strong convergence theory under the local Lipschitz condition plus the Khasminskii-type condition. The key aim of this paper is to establish the rate of strong convergence of the truncated Euler–Maruyama method for one-dimensional stochastic differential equations involving that the local time at point zero under the drift coefficient satisfies a one-sided Lipschitz condition and plus some additional conditions.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"31 1","pages":"141 - 152"},"PeriodicalIF":0.3000,"publicationDate":"2023-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Random Operators and Stochastic Equations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/rose-2023-2003","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract Recently, Mao developed a new explicit method, called the truncated Euler–Maruyama method for nonlinear SDEs, and established the strong convergence theory under the local Lipschitz condition plus the Khasminskii-type condition. The key aim of this paper is to establish the rate of strong convergence of the truncated Euler–Maruyama method for one-dimensional stochastic differential equations involving that the local time at point zero under the drift coefficient satisfies a one-sided Lipschitz condition and plus some additional conditions.