Abstract:

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 ［t₀,∞), further, the estimate of the error between the approximate solution and the accurate solution has been obtained, where t₀ is a positive number.

Key words: stochastic functional differential equations, infinite delay, existence, uniqueness