Transportation inequalities for mean-field neutral stochastic functional differential equation driven by a  fractional  Brownian motion

Salah Hajji; Ahmed  Lahmoudi; El Hassan Lakhel

doi:10.56947/amcs.v18.203

Authors

Salah Hajji Department of Mathematics, Regional Center for the Professions of Education and Training, Morocco
Ahmed Lahmoudi Cadi Ayyad University, National School of Applied Sciences, Morocco
El Hassan Lakhel Cadi Ayyad University, National School of Applied Sciences, Morocco

DOI:

https://doi.org/10.56947/amcs.v18.203

Keywords:

Mild solution, Fractional Brownian motion, Wiener integral, Girsanov transformation, Transportation inequality

Abstract

In this paper we demonstrate the uniqueness and existence of a mild solution for a mean-field neutral stochastic differential equation that involves finite delay. The equation is driven by a fractional Brownian motion with Hurst parameter H>1/2 in a Hilbert space. Additionally, we establish the transportation inequalities for the law of the mild solution, with respect to the uniform distance.