Optimal control of the FitzHugh-Nagumo stochastic model with nonlinear diffusion

Abstract: 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.