THE INVARIANT MEASURE OF RANDOM WALKS IN THE QUARTER-PLANE: REPRESENTATION IN GEOMETRIC TERMS
2015 ◽
Vol 29
(2)
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pp. 233-251
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Keyword(s):
We consider the invariant measure of homogeneous random walks in the quarter-plane. In particular, we consider measures that can be expressed as a finite linear combination of geometric terms and present conditions on the structure of these linear combinations such that the resulting measure may yield an invariant measure of a random walk. We demonstrate that each geometric term must individually satisfy the balance equations in the interior of the state space and further show that the geometric terms in an invariant measure must have a pairwise-coupled structure. Finally, we show that at least one of the coefficients in the linear combination must be negative.
1991 ◽
Vol 43
(2)
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pp. 241-250
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1960 ◽
Vol 56
(4)
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pp. 322-328
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2014 ◽
Vol 10
(06)
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pp. 1395-1420
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1980 ◽
pp. 223-233
2012 ◽
Vol 15
◽
pp. 444-462
1978 ◽
Vol 30
(02)
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pp. 289-300
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Keyword(s):
1969 ◽
Vol 10
(3-4)
◽
pp. 335-340
Keyword(s):
2003 ◽
Vol 17
(3)
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pp. 369-395
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Keyword(s):