Large deviation principle for reflected diffusion process fractional Brownian motion

Year 2021, Volume: 5 Issue: 1, 127 - 137, 31.03.2021

Raphael Diatta Ibrahima Sane , Alassane Diédhiou

https://doi.org/10.31197/atnaa.767867

Abstract

In this paper we establish a large deviation principle for solution of perturbed reflected stochastic
differential equations driven by a fractional Brownian motion B^H with Hurst index H ∈ (0;1).
The key is to prove a uniform Freidlin-Wentzell estimates of solution on the set of continuous
square integrable functions in the dual of Schwartz space . We have built in the whole interval of H ∈ (0;1) a new approch different from that of Y. Inahama [10] for LDP of εBH in [6].Thanks to this we establish the LDP for the process diffusion of reflected stochastic differential
equations via the principle of contraction on the set of continuous square integrable functions in the dual of
Schwartz space.The existence and uniqueness of the solutions of such equations (1) and (2) are obtained by [7].

Keywords

Fractional Brownian motion, Large deviation principle, Contraction principle, Reflected stochastic differential equation, Skorohod problem

Supporting Institution

Assane SECK University of Ziguinchor,

Project Number

6

Thanks

We would like to thank the UASZ and the Laboratory of Mathematics and Application

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