The Annals of Applied Probability

On the Karlin-McGregor theorem and applications

W. Böhm and S. G. Mohanty

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In this paper we present some interesting results which follow from the celebrated determinant formulas for noncoincidence probabilities of Markov processes discovered by Karlin and McGregor. The first theorem is a determinant formula for the probability that a Markov jump process will avoid a certain finite set of points. From this theorem a simple solution of the moving boundary problem for certain types of Markov processes can be obtained. The other theorems deal with noncoincidence probabilities of sets of random walks which need not be identically distributed. These formulas have interesting applications, especially in the theory of queues.

Article information

Ann. Appl. Probab. Volume 7, Number 2 (1997), 314-325.

First available in Project Euclid: 14 October 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60C05: Combinatorial probability 60J15

Noncoincidence probabilities moving boundaries order statistics queueing


Böhm, W.; Mohanty, S. G. On the Karlin-McGregor theorem and applications. Ann. Appl. Probab. 7 (1997), no. 2, 314--325. doi:10.1214/aoap/1034625333.

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