C_g空间中无限时滞随机泛函微分方程解的存在唯一性

选取空间Cg为相空间,考察具有无限时滞随机泛函微分方程解的存在唯一性,利用Picard迭代序列、伊藤公式以及Doob鞅不等式,得到了无限时滞随机泛函微分方程的解在区间[t0,∞)上的存在性与唯一性,进而得到了近似解与精确解之间的误差估计,其中t0为正常数.

Existence and Uniqueness of Solutions for Stochastic Functional Differential Equations with Infinite Delay at Phase Space C_g

With space C_g as phase space,the existence and uniqueness of the solutions for stochastic functional differential equations with infinite delay were considered. By means of Picard iterative sequence,Ito formula and Doob martingale inequality,it has been proved that stochastic functional differential equation with infinite delay has a unique solution at the interval [t_0,∞),further,the estimate of the error between the approximate solution and the accurate solution has been obtained,where t_0 is a positive number.