Non - Stationary Stochastic Point - Process Models in Neurophysiology with Applications to Learning

For the study of discharge activities of neurons, appropriate-ness and the basic role of certain non-stationary stochastic point-process models are appraised. Measures of association (cross-correlations) of spike trains for two or more neurons are also considered. Incorporating random intensity functions, some doubly stochastic Poisson process representations for the counting processes (and histogram processes) arising in the context of spike trains are studied under appropriate regularity assumptions (quite plausible in a real situation). Applications to synaptic plasticity as a model for neural learning are also discussed.