{"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":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":2.5000,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fractional Calculus and Applied Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s13540-024-00334-9","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","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。
期刊介绍：
Fractional Calculus and Applied Analysis (FCAA, abbreviated in the World databases as Fract. Calc. Appl. Anal. or FRACT CALC APPL ANAL) is a specialized international journal for theory and applications of an important branch of Mathematical Analysis (Calculus) where differentiations and integrations can be of arbitrary non-integer order. The high standards of its contents are guaranteed by the prominent members of Editorial Board and the expertise of invited external reviewers, and proven by the recently achieved high values of impact factor (JIF) and impact rang (SJR), launching the journal to top places of the ranking lists of Thomson Reuters and Scopus.
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