Relationship between event counting statistics and waiting time statistics in the steady state
Statistical Mechanics
2023-11-02 v1
Abstract
There are two main quantities involved in the deviation of a stochastic process from a Poisson process: the squared coefficient of variation of the time intervals between adjacent events and the Fano factor of the number of reaction events. As well known, these two quantities are equal for renewal processes, while their relationship remains unexplored for non-renewal processes. In this paper, we establish an explicit relation between the two statistics that is applicable to non-renewal processes. The new relation, which reduces to the previously mentioned result for renewal processes, is confirmed to be accurate in several cases of non-renewal processes.
Keywords
Cite
@article{arxiv.2311.00538,
title = {Relationship between event counting statistics and waiting time statistics in the steady state},
author = {Seong Jun Park and M. Y. Choi},
journal= {arXiv preprint arXiv:2311.00538},
year = {2023}
}