The Annals of Probability

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

F. K. Hwang

Full-text: Open access

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.

Article information

Source
Ann. Probab., Volume 5, Number 5 (1977), 814-817.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176995725

Digital Object Identifier
doi:10.1214/aop/1176995725

Mathematical Reviews number (MathSciNet)
MR471014

Zentralblatt MATH identifier
0375.60076

JSTOR
links.jstor.org

Subjects
Primary: 60J05: Discrete-time Markov processes on general state spaces
Secondary: 60E05: Distributions: general theory

Keywords
Coincidence probabilities Markov process stopping time cluster generalized birthday problem

Citation

Hwang, F. K. A Generalization of the Karlin-McGregor Theorem on Coincidence Probabilities and an Application to Clustering. Ann. Probab. 5 (1977), no. 5, 814--817. doi:10.1214/aop/1176995725. https://projecteuclid.org/euclid.aop/1176995725


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