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May 1997 On the Karlin-McGregor theorem and applications
W. Böhm, S. G. Mohanty
Ann. Appl. Probab. 7(2): 314-325 (May 1997). DOI: 10.1214/aoap/1034625333


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.


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W. Böhm. S. G. Mohanty. "On the Karlin-McGregor theorem and applications." Ann. Appl. Probab. 7 (2) 314 - 325, May 1997.


Published: May 1997
First available in Project Euclid: 14 October 2002

zbMATH: 0884.60010
MathSciNet: MR1442315
Digital Object Identifier: 10.1214/aoap/1034625333

Primary: 60C05 , 60J15

Keywords: moving boundaries , Noncoincidence probabilities , order statistics , Queueing

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.7 • No. 2 • May 1997
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