{"title":"分数布朗运动驱动的麦金-弗拉索夫 SDE 的福克-普朗克方程","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":"{\"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}","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}
Fokker-Planck equations for McKean-Vlasov SDEs driven by fractional Brownian motion
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.