LARGE DEVIATION FOR SEVERAL FRACTIONAL BROWNIAN MOTIONS AND DIFFUSION PROCESS
Keywords:
fractional Brownian motion, large deviations principle, mixed fractional Brownian motion.DOI:
https://doi.org/10.17654/0975045224003Abstract
We examine the asymptotic behavior of a solution of a differential equation derived by several independent fractional Brownian motions with Hurst index $H \in(0 ; 1)$. We show the large deviations first for the linear combination of several fractional Brownian motions. Through this first step, the contraction principle allows us to study via the large deviations the behavior of the considered solution.
Received: September 18, 2023
Revised: November 3, 2023
Accepted: November 24, 2023
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