Title: On a Fractional Stochastic Hodgkin-Huxley Model,
Abstract: The model studied in this paper is a stochastic extension of the so-called
neuron model introduced by Hodgkin and Huxley. In the sense of rough paths, the
model is perturbed by a multiplicative noise driven by a fractional Brownian
motion, with a vector field satisfying the viability condition of Coutin and
Marie for $\mathbb R\times [0,1]^3$. An application to the modeling of the
membrane potential of nerve fibers damaged by a neuropathy is provided.