Interevent-time statistics for shot-noise-driven self-exciting point processes in photon detection

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Abstract
Probability densities for interevent time are obtained for a doubly stochastic Poisson point process (DSPP) in the presence of self-excitation. The DSPP is assumed to have a stochastic rate that is a filtered Poisson point process (shot noise). The model of a Poisson process driving another Poisson process produces a pulse-bunching effect. Self-excitation (relative refractoriness) results in a deficit of short time intervals. Both effects are observed in many applications of optical detection. The model is applicable to the detection of fluorescence or scintillation generated by ionizing radiation in a photomultiplier tube. It is also used successfully to fit the maintained discharge interspike-interval histograms recorded by Barlow, Levick, and Yoon [ Vision Res. 11, Suppl. 3, 87– 101 ( 1971)] for a cat’s on-center retinal ganglion cell in darkness.