{"title":"Non-confluence for SDEs driven by fractional Brownian motion with Markovian switching","authors":"Zhi Li, Benchen Huang, Liping Xu","doi":"10.1007/s13540-024-00334-9","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we investigate the non-confluence property of a class of stochastic differential equations with Markovian switching driven by fractional Brownian motion with Hurst parameter <span>\\(H\\in (1/2,1)\\)</span>. By using the generalized Itô formula and stopping time techniques, we obtain some sufficient conditions ensuring the non-confluence property for the considered equations. Additionally, we present two important corollaries on the non-confluence property by the Poisson equation and <i>M</i>-matrix, respectively, which can verify the non-confluence property more effectively than the general condition. Finally, we provide an example to illustrate the practical usefulness of our theoretical results.</p>","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s13540-024-00334-9","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we investigate the non-confluence property of a class of stochastic differential equations with Markovian switching driven by fractional Brownian motion with Hurst parameter \(H\in (1/2,1)\). By using the generalized Itô formula and stopping time techniques, we obtain some sufficient conditions ensuring the non-confluence property for the considered equations. Additionally, we present two important corollaries on the non-confluence property by the Poisson equation and M-matrix, respectively, which can verify the non-confluence property more effectively than the general condition. Finally, we provide an example to illustrate the practical usefulness of our theoretical results.
在本文中,我们研究了一类具有马尔可夫切换的随机微分方程,该方程由具有赫斯特参数(H\in (1/2,1)\)的分数布朗运动驱动。通过使用广义伊托公式和停止时间技术,我们得到了一些确保所考虑方程非融合特性的充分条件。此外,我们还通过泊松方程和 M 矩阵分别提出了关于非汇合性质的两个重要推论,它们比一般条件更有效地验证了非汇合性质。最后,我们提供了一个例子来说明我们的理论结果的实用性。