Large deviation principle for reflected diffusion process fractional Brownian motion

Open Access

Original research article

Author(s):

Raphael Diatta, Ibrahima Sané, Alassane Diédhiou

Department of Mathematics, Laboratory of Mathematics and Applications, UFR Sciences and Technologies, Assane Seck University of Ziguinchor, BP 523 – Ziguinchor, Senegal.

Advances in the Theory of Nonlinear Analysis and its Applications 5(1), 127-137.

Received: July 10, 2020

Accepted: January 15, 2021

Published: January 20, 2021

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, Skorokhod problem.

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APA Style

Diatta, R., Sane, I., & Diédhiou, A. (2021). Large deviation principle for reflected diffusion process fractional Brownian motion. Advances in the Theory of Nonlinear Analysis and its Application, 5(1), 127-137.