Large Deviations For Nonlinear Neutral Delay Stochastic Differential Equations

Neutral stochastic delay differential equations are special stochastic differentialequations,which not only depend on present and past states but also involve derivativeswith delays.Neutral stochastic delay differential equations have an important applica-tions in many areas such as the chemical engineering systems, the theory of aeroelas-ticity.The aim of this paper is to consider the large deviations for neutral stochasticdelay differential equations. This article is divided into three chapters.In chapter 1, we present the background and significance of large deviations ofnonlinear neutral delay stochastic equation, the large deviation principle and the mainwork of this paper.In chapter 2,some preparations are given.We mainly introduce some conceptson large deviations for stochastic differential equations such as the Brownian motionsample path large deviations, Freidlin-Wentzell theory ,etc.In chapter 3,we study large deviation of nonlinear neutral stochastic differentialequations, and we establish upper and lower large deviations estimates by constructinga series of lemmas.