Journal of Statistical Physics, Vol. 77, Nos. 3/4, 1994, p. 733-754.
Models for growth in disordered media, which are deterministic once the random environment is specified, can be transformed into stochastic growth processes with a time-dependent noise. The mapping generally induces a memory in the stochastic process. This transformation is proposed and discussed in detail. An approximation scheme is worked out analytically and possible applications are discussed.