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.
Publié le : 1997-05-14
Classification:
Noncoincidence probabilities,
moving boundaries,
order statistics,
queueing,
60C05,
60J15
@article{1034625333,
author = {B\"ohm, W. and Mohanty, S. G.},
title = {On the Karlin-McGregor theorem and applications},
journal = {Ann. Appl. Probab.},
volume = {7},
number = {1},
year = {1997},
pages = { 314-325},
language = {en},
url = {http://dml.mathdoc.fr/item/1034625333}
}
Böhm, W.; Mohanty, S. G. On the Karlin-McGregor theorem and applications. Ann. Appl. Probab., Tome 7 (1997) no. 1, pp. 314-325. http://gdmltest.u-ga.fr/item/1034625333/