Stochastic stability of a system of perfect integrate-and-fire inhibitory neurons (Q779161)

The model of a (perfect) stochastic integrate-and-fire neuron evolves according to the stochastic differential equation \[ dZ_i(t)=I(t)+\sigma\,dW_i(t), \] where \(I\) is the neural input, the diffusion coefficient \(\sigma\) is constant and \(W_i\) is a Brownian motion. The author considers fluid limits, see [\textit{J. G. Dai}, Ann. Appl. Probab. 5, No. 1, 49--77 (1995; Zbl 0822.60083); \textit{A. L. Stolyar}, Markov Process. Relat. Fields 1, No. 4, 491--512 (1995; Zbl 0902.60079)] and proves piecewise linearity and the convergence to the stationary distribution in the total variation norm.