{"title":"Fokker-Planck equations for McKean-Vlasov SDEs driven by fractional Brownian motion","authors":"Saloua Labed, Nacira Agram, Bernt Oksendal","doi":"arxiv-2409.07029","DOIUrl":null,"url":null,"abstract":"In this paper, we study the probability distribution of solutions of\nMcKean-Vlasov stochastic differential equations (SDEs) driven by fractional\nBrownian motion. We prove the associated Fokker-Planck equation, which governs\nthe evolution of the probability distribution of the solution. For the case\nwhere the distribution is absolutely continuous, we present a more explicit\nform of this equation. To illustrate the result we use it to solve specific\nexamples, including the law of fractional Brownian motion and the geometric\nMcKean-Vlasov SDE, demonstrating the complex dynamics arising from the\ninterplay between fractional noise and mean-field interactions.","PeriodicalId":501245,"journal":{"name":"arXiv - MATH - Probability","volume":"101 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Probability","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.07029","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we study the probability distribution of solutions of
McKean-Vlasov stochastic differential equations (SDEs) driven by fractional
Brownian motion. We prove the associated Fokker-Planck equation, which governs
the evolution of the probability distribution of the solution. For the case
where the distribution is absolutely continuous, we present a more explicit
form of this equation. To illustrate the result we use it to solve specific
examples, including the law of fractional Brownian motion and the geometric
McKean-Vlasov SDE, demonstrating the complex dynamics arising from the
interplay between fractional noise and mean-field interactions.