Abstract:

Under the uniform Lipschitz condition, weakened linear growth condition and contractive condition, the existenceuniqueness and error estimation of the solution to neutral stochastic functional differential equations with infinite delay in space C_h were investigated. The existenceuniqueness theorem was obtained by means of Picard iteration and Doob’s martingale inequality. Furthermore, the continuous dependence of the solution on the initial data and the error estimation between the approximation solution and the exact solution were given.

Key words: neutral stochastic functional differential equations; space C_h, existenceuniqueness, error estimation