Correlations In Sequences Of First-Passage Times

Abstract

The correlations in the sequence of first‐passage times (FPTs) is discussed for two noise‐driven systems. First, results for a perfect integrate‐and‐fire neuron driven by dichotomous process (DP) are reviewed. The FPT sequence in this case corresponds to the interspike intervals separating neural voltage discharges (action potentials). Furthermore, simulation results for the correlations of residence times in a bistable potential driven by a DP are presented. In both systems, the amplitude of correlations in the FPTs sequence decays exponentially with a rate inversely proportional to the correlation time of the driving process. While the neuron model shows a strictly positive correlation between all FPTs, the bistable system displays correlations that oscillate with the lag between intervals.