On the solution of stochastic functional differential equations via memory gap

We present an alternative proof for the existence of solutions of stochastic functional differential equations satisfying a global Lipschitz condition. The proof is based on an approximation scheme in which the continuous path dependence does not go up to the present: there is a memory gap. Strong convergence is obtained by closing the gap. Such approximation is particularly useful when extending stochastic models with discrete delay to models with continuous full finite memory.