Homogenization of infinite dimensional diffusion processes with periodic drift coefficients

A homogenization problem of infinite dimensional diffusion processes indexed by Z having periodic drift coefficients is considered. By making use of an approximation sequence that converges to the original infinite dimensional diffusion process, the homogenization problem in a generalized sense is discussed. Here, the scaling limit of the original process is not taken directly, but the scaling limit of an approximation sequence, whose running index is controlled by the parameter of the scaling limit, is taken. The existence of a non trivial limiting process which is an infinite dimensional diffusion having constant coefficients is shown.