A stochastic dynamics viewpoint of some neuron models

This paper is an overview of some recent work on stochastic neuron models. As a probabilist, my approach is to first try to understand the dynamics of the neuron model and then ask what are the important ways in which the natural stochastic nature of real neurons will interact with the dynamics to produce some aspect of the input-output relation observed in experiments. My primary interest has been in the leaky-integrate-and-fire (LIF) and the stochastic Morris-Lecar (ML) neuron models.