Refractory effects in neural counting processes with exponentially decaying rates

The effect of nonparalyzable dead time on Poisson point processes with random integrated rates is studied. The case of exponentially decreasing rate, plus background (pedestal), with a uniformly uncertain starting time is explicitly presented. The decay time is considered to be slow compared to the refractory time. No constraints on the sampling time are imposed for calculating the mean and variance, though for the counting distribution, the sampling time must be short compared to the decay time. The results are expected to be useful in neurobiology, neural counting, psychophysics, photon counting, nuclear counting, and radiochemistry.