A central limit theorem for the stochastic cable equation

Abstract

We study one-dimensional nonlinear stochastic cable equations driven by a multiplicative space-time white noise. Using the Malliavin-Stein method, we prove a central limit theorem for the spatial average of the solution. The convergence is established in the total variation distance with mild conditions. We also establish a functional central limit theorem with a technical assumption. Furthermore, we show that this assumption holds in a special case.