{"title":"Mixed slow-fast stochastic differential equations: Averaging principle result","authors":"Shitao Liu","doi":"10.1007/s13540-024-00368-z","DOIUrl":null,"url":null,"abstract":"<p>This paper investigates stochastic averaging principle for a class of mixed slow-fast stochastic differential equations driven simultaneously by a multidimensional standard Brownian motion and a multidimensional fractional Brownian motion with Hurst parameter <span>\\(1/2<H<1\\)</span>. The stochastic averaging principle shows that the slow component strongly converges to the solution of the corresponding averaged equations under a weaker condition than the Lipschitz one.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"7 1","pages":""},"PeriodicalIF":2.9000,"publicationDate":"2025-01-17","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/s13540-024-00368-z","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
This paper investigates stochastic averaging principle for a class of mixed slow-fast stochastic differential equations driven simultaneously by a multidimensional standard Brownian motion and a multidimensional fractional Brownian motion with Hurst parameter \(1/2<H<1\). The stochastic averaging principle shows that the slow component strongly converges to the solution of the corresponding averaged equations under a weaker condition than the Lipschitz one.
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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