In the applications one is given the matrix A and it is required to con-
structP(t) and to study the propertiesof the corresponding stochastic proc-
ess. The existence,uniqueness, and the analytic properties of P(t) have been
discussed in detail in I. The objective of this paper is to use the resultsof
1 to establish equivalences between properties of the stochastic process
and properties thesequencesXn , n,u and to evaluate,in terms these
of of
sequences, some of the interesting probabilisticquantities associated with the
process.
%0 Journal Article
%1 karlin3
%A Karlin, Samuel
%A McGregor, James
%D 1957
%J Trans. Amer. Math. Soc.
%K birth_death_processes orthogonal_polynomials
%P 366--400
%T The classification of birth and death processes
%U http://www.jstor.org/stable/1993021
%V 86
%X In the applications one is given the matrix A and it is required to con-
structP(t) and to study the propertiesof the corresponding stochastic proc-
ess. The existence,uniqueness, and the analytic properties of P(t) have been
discussed in detail in I. The objective of this paper is to use the resultsof
1 to establish equivalences between properties of the stochastic process
and properties thesequencesXn , n,u and to evaluate,in terms these
of of
sequences, some of the interesting probabilisticquantities associated with the
process.
@article{karlin3,
abstract = { In the applications one is given the matrix A and it is required to con-
structP(t) and to study the propertiesof the corresponding stochastic proc-
ess. The existence,uniqueness, and the analytic properties of P(t) have been
discussed in detail in [I]. The objective of this paper is to use the resultsof
[1] to establish equivalences between properties of the stochastic process
and properties thesequences{Xn }, { n,u and to evaluate,in terms these
of } of
sequences, some of the interesting probabilisticquantities associated with the
process.
},
added-at = {2010-11-02T15:40:02.000+0100},
author = {Karlin, Samuel and McGregor, James},
biburl = {https://www.bibsonomy.org/bibtex/2dca8f0969fa0516ad591f2592e7f7822/peter.ralph},
description = {q-paper},
fjournal = {Transactions of the American Mathematical Society},
interhash = {537c6cd3692f2045597ee0403d3f97c5},
intrahash = {dca8f0969fa0516ad591f2592e7f7822},
issn = {0002-9947},
journal = {Trans. Amer. Math. Soc.},
keywords = {birth_death_processes orthogonal_polynomials},
mrclass = {60.00 (34.00)},
mrnumber = {MR0094854 (20 \#1363)},
mrreviewer = {D. G. Kendall},
pages = {366--400},
timestamp = {2010-11-02T15:40:02.000+0100},
title = {The classification of birth and death processes},
url = {http://www.jstor.org/stable/1993021},
volume = 86,
year = 1957
}