A result on the first-passage time of an Ornstein–Uhlenbeck process

A review of the methods for signal estimation in stochastic diffusion leaky integrate-and-fire neuronal models

Parameters in diffusion neuronal models are divided into two groups; intrinsic and input parameters. Intrinsic parameters are related to the properties of the neuronal membrane and are assumed to be known throughout the paper. Input parameters characterize processes generated outside the neuron and methods for their estimation are reviewed here. Two examples of the diffusion neuronal model, which are based on the integrate-and-fire concept, are investigated--the Ornstein--Uhlenbeck model as the most common one and the Feller model as an illustration of state-dependent behavior in modeling the neuronal input. Two types of experimental data are assumed-intracellular describing the membrane trajectories and extracellular resulting in knowledge of the interspike intervals. The literature on estimation from the trajectories of the diffusion process is extensive and thus the stress in this review is set on the inference made from the interspike intervals.