115 citations · 782 across the 69 of their papers we have counts for
75 papers
The Bernoulli clock: probabilistic and combinatorial interpretations of the Bernoulli polynomials by circular convolution
Yassine El Maazouz, Jim Pitman
The factorially normalized Bernoulli polynomials are known to be characterized by and for is the antiderivative of su…
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…
Hidden symmetries and limit laws in the extreme order statistics of the Laplace random walk
Jim Pitman, Wenpin Tang
This paper is concerned with the limit laws of the extreme order statistics derived from a symmetric Laplace walk. We provide two different descriptions of the point process of the…
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…
Markovian structure in the concave majorant of Brownian motion
Mehdi Ouaki, Jim Pitman
The purpose of this paper is to highlight some hidden Markovian structure of the concave majorant of the Brownian motion. Several distributional identities are implied by the joint…
Extreme order statistics of random walks
Jim Pitman, Wenpin Tang
This paper is concerned with the limit theory of the extreme order statistics derived from random walks. We establish the joint convergence of the order statistics near the minimum…