  We consider the existence and first order conditions of optimality for a
stochastic optimal control problem inspired by the celebrated FitzHugh-Nagumo
model, with nonlinear diffusion term, perturbed by a linear multiplicative
Brownian-type noise. The main novelty of the present paper relies on the
application of the {\it rescaling method} which allows us to reduce the
original problem to a random optimal one.
