Stability Analysis Of Solution For Stochastic Delay Differential Equations Driven By Fractional Brownian Motion

As an important stochastic process,fractional Brownian motion is widely used in atmospheric sciences,financial engineering and other fields because of its unique properties.Therefore,it is of great significance to study stochastic differ-ential equations driven by fractional Brownian motion.In this paper we consider the existence,uniqueness and mean square exponential stability of solutions for stochastic delay differential equations driven by fractional Brownian motion.We first discuss the existence,uniqueness and mean square exponential sta-bility of the mild solution for equation with Hurst parameter?(0,1).In order to obtain the consistent result of?(0,1),we introduce an important lemma to estimate the random term and obtain the existence and uniqueness of the solution.A generalized integral inequality is used to prove the mean square exponential sta-bility of the mild solution,and two numerical examples are given to illustrate our results.Then we study the existence,uniqueness and mean square exponential sta-bility of the entire solutions for linear equations and non-linear equations when Hurst parameter>₁/2.Before proving the uniqueness of the entire solution for linear equation,we prove a factorization formula,which can be used to show that the entire solution is almost surely continuous.And further illustrate the uniqueness and stability of the entire solution.The H(?)lder continuity of the entire solution is also addressed.Based on the study of linear equations,we construct a unique sequence and prove that the sequence converges to the entire solution of non-linear equation.Therefore,we obtain the existence,uniqueness and the H(?)lder continuity of the entire solution for non-linear equation.Finally,we obtain the stability of the entire solution by using the generalized integral inequality.