We examine the asymptotic behavior of a solution of a differential equation derived by several independent fractional Brownian motions with Hurst index  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.

fractional Brownian motion, large deviations principle, mixed fractional Brownian motion.

Received: September 18, 2023;  Revised: November 3, 2023;  Accepted: November 24, 2023

How to cite this article: Raphaël DIATTA and Alassane DIEDHIOU, Large deviation for several fractional Brownian motions and diffusion process, International Journal of Numerical Methods and Applications 24(1) (2024), 31-44. http://dx.doi.org/10.17654/0975045224003

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