  The problem of pattern formation in a generic two species reaction--diffusion
model is studied, under the hypothesis that only one species can diffuse. For
such a system, the classical Turing instability cannot take place. At variance,
by working in the generalized setting of a stochastic formulation to the
inspected problem, Turing like patterns can develop, seeded by finite size
corrections. General conditions are given for the stochastic Turing patterns to
occur. The predictions of the theory are tested for a specific case study.
