Stochastic Monotonicity and Queueing Applications of Birth-Death Processes
Erik van Doorn
Dec 2012 · Lecture Notes in Statistics Book 4 · Springer Science & Business Media
Ebook
118
Pages
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About this ebook
A stochastic process {X(t): 0 S t =} with discrete state space S c ~ is said to be stochastically increasing (decreasing) on an interval T if the probabilities Pr{X(t) i}, i E S, are increasing (decreasing) with t on T. Stochastic monotonicity is a basic structural property for process behaviour. It gives rise to meaningful bounds for various quantities such as the moments of the process, and provides the mathematical groundwork for approximation algorithms. Obviously, stochastic monotonicity becomes a more tractable subject for analysis if the processes under consideration are such that stochastic mono tonicity on an inter val 0
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