Quasi-Birth-and-Death Processes, Lattice Path Counting, and Hypergeometric Functions
2009 ◽
Vol 46
(2)
◽
pp. 507-520
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Keyword(s):
In this paper we consider a class of quasi-birth-and-death processes for which explicit solutions can be obtained for the rate matrix R and the associated matrix G. The probabilistic interpretations of these matrices allow us to describe their elements in terms of paths on the two-dimensional lattice. Then determining explicit expressions for the matrices becomes equivalent to solving a lattice path counting problem, the solution of which is derived using path decomposition, Bernoulli excursions, and hypergeometric functions. A few applications are provided, including classical models for which we obtain some new results.
2009 ◽
Vol 46
(02)
◽
pp. 507-520
◽
2016 ◽
Vol 53
(1)
◽
pp. 106-120
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1979 ◽
1993 ◽
Vol 14
(1)
◽
pp. 43-51
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1994 ◽
Vol 68
(1)
◽
pp. 215-217
1980 ◽
Vol 143
(4)
◽
pp. 524
2018 ◽
Vol 21
(4)
◽
pp. 1119-1149
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Keyword(s):