Fokker-Planck equations for McKean-Vlasov SDEs driven by fractional Brownian motion

Autor:	Labed, Saloua, Agram, Nacira, Oksendal, Bernt
Rok vydání:	2024
Předmět:	Mathematics - Probability
Druh dokumentu:	Working Paper
Popis:	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. Comment: 21 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2409.07029 Zobrazit plný text záznamu View this record from Arxiv