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math.PR2021
The range of a self-similar additive gamma process is a scale invariant Poisson point process
Jim Pitman, Zhiyi You
It is shown that for a non-decreasing self-similar stochastic process with independent increments, the range of forms a Poisson point process with -finite intensity if a…
math.PR2021
Stationary 1-dependent Counting Processes: from Runs to Bivariate Generating Functions
Jim Pitman, Zhiyi You
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…