The temporal patterns of action potentials fired by a two-point stochastic neuron model were investigated. In this model the membrane potential of the dendritic compartment follows the Orstein-Uhlenbeck process and is not affected by the spiking activity. The axonal compartment, corresponding to the spike initiation site, is described by a simplified RC circuit. Estimators of the mean and variance of the input, based on a sampling of the axonal membrane potential, were derived and applied to simulated data. The dependencies of the mean firing frequency and of the coefficient of variation and serial correlation of interspike intervals on the mean and variance of the input were also studied by computer simulation in both 1- and 2-point models. The main property distinguishing the 2-point model from the classical 1-point model is its ability to produce clusters of short (or long) intervals between spikes under conditions of constant stimulation, as often observed in real neurons. It is shown that the nearly linear frequency response of the neuron, starting with subthreshold values of the input, is accounted for by the variability of the input (noise), which indicates that noise can play a positive role in nervous systems. The linear response frequency with respect to noise of the models suggests that the neuron can function as a noise encoder.