A Generalization of the Karlin-McGregor Theorem on Coincidence Probabilities and an Application to Clustering

Abstract

Karlin and McGregor calculated the coincidence probabilities for $n$ particles independently executing a Markov process of a certain class. This note extends their result by allowing the particles to have different stopping times. Applied to a one-dimensional clustering problem, this gives a new solution computationally simpler than previous ones.