{"title":"Moderate deviations for rough differential equations","authors":"Yuzuru Inahama, Yong Xu, Xiaoyu Yang","doi":"10.1112/blms.13097","DOIUrl":null,"url":null,"abstract":"<p>Small noise problems are quite important for all types of stochastic differential equations. In this paper, we focus on rough differential equations driven by scaled fractional Brownian rough path with Hurst parameter <span></span><math>\n <semantics>\n <mrow>\n <mi>H</mi>\n <mo>∈</mo>\n <mo>(</mo>\n <mn>1</mn>\n <mo>/</mo>\n <mn>4</mn>\n <mo>,</mo>\n <mn>1</mn>\n <mo>/</mo>\n <mn>2</mn>\n <mo>]</mo>\n </mrow>\n <annotation>$H\\in (1/4, 1/2]$</annotation>\n </semantics></math>. We prove a moderate deviation principle for this equation as the scale parameter tends to zero.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 8","pages":"2738-2748"},"PeriodicalIF":0.8000,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the London Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/blms.13097","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Small noise problems are quite important for all types of stochastic differential equations. In this paper, we focus on rough differential equations driven by scaled fractional Brownian rough path with Hurst parameter . We prove a moderate deviation principle for this equation as the scale parameter tends to zero.
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