  Interspike intervals describe the output of neurons. Signal transmission in a
neuronal network implies that the output of some neurons becomes the input of
others. The output should reproduce the main features of the input to avoid a
distortion when it becomes the input of other neurons, that is input and output
should exhibit some sort of consistency. In this paper, we consider the
question: how should we mathematically characterize the input in order to get a
consistent output? Here we interpret the consistency by requiring the
reproducibility of the input tail behaviour of the interspike intervals
distributions in the output. Our answer refers to a system of interconnected
neurons with stochastic perfect integrate and fire units. In particular, we
show that the class of regularly-varying vectors is a possible choice to obtain
such consistency. Some further necessary technical hypotheses are added.
