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arXiv · 2105.08255

Stationary 1-dependent Counting Processes: from Runs to Bivariate Generating Functions

Jim Pitman·Zhiyi You
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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.

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Jim Pitman, Zhiyi You. 2021-05-18. Stationary 1-dependent Counting Processes: from Runs to Bivariate Generating Functions. https://arxiv.org/abs/2105.08255

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