Interval distribution of a stationary point process (Q1803361)

The following stochastic model for neuron firing is considered. Let be given two interacting random point processes on the real line. One of them describes the arrival epochs of stimuli (the primary excitatory process), and one the arrival epochs of inhibitors. The inhibitors delete the stimuli according to a given rule. The interarrival distribution of the undeleted stimuli is determined under the assumption that the two input processes are independent and recurrent and that at least one of the input processes has an interarrival distribution of a specific type, e.g. a special Erlang distribution.