Large deviation principle for reflected diffusion process fractional Brownian motion

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

Kaynakça

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