## The Annals of Applied Probability

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

### On the Karlin-McGregor theorem and applications

W. Böhm and S. G. Mohanty

#### Abstract

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

**Source**

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

**Dates**

First available in Project Euclid: 14 October 2002

**Permanent link to this document**

http://projecteuclid.org/euclid.aoap/1034625333

**Mathematical Reviews number (MathSciNet)**

MR1442315

**Digital Object Identifier**

doi:10.1214/aoap/1034625333

**Zentralblatt MATH identifier**

0884.60010

**Subjects**

Primary: 60C05: Combinatorial probability 60J15

**Keywords**

Noncoincidence probabilities moving boundaries order statistics queueing

#### Citation

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. http://projecteuclid.org/euclid.aoap/1034625333.