Stationary 1-dependent Counting Processes: from Runs to Bivariate Generating Functions
Probability
2021-05-19 v1
Abstract
We give a formula for the bivariate generating function of a stationary 1-dependent counting process in terms of its run probability generating function, with a probabilistic proof. The formula reduces to the well known bivariate generating function of the Eulerian distribution in the case of descents of a sequence of indepependent and identically distributed random variables. The formula is compared with alternative expressions from the theory of determinantal point processes and the combinatorics of sequences.
Cite
@article{arxiv.2105.08255,
title = {Stationary 1-dependent Counting Processes: from Runs to Bivariate Generating Functions},
author = {Jim Pitman and Zhiyi You},
journal= {arXiv preprint arXiv:2105.08255},
year = {2021}
}
Comments
17 pages