Stochastic monotonicity of birth–death processes
- 1 March 1980
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 12 (1) , 59-80
- https://doi.org/10.2307/1426494
Abstract
A birth–death process {x(t):t≥ 0} with state space the set of non-negative integers is said to be stochastically increasing (decreasing) on the interval (t1,t2) if Pr {x(t) >i} is increasing (decreasing) withton (t1,t2) for alli= 0, 1, 2, ···. We study the problem of finding a necessary and sufficient condition for a birth–death process with general initial state probabilities to be stochastically monotone on an interval. Concrete results are obtained when the initial distribution vector of the process is a unit vector. Fundamental in the analysis, and of independent interest, is the concept of dual birth–death processes.Keywords
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