Published online by Cambridge University Press: 14 July 2016
Particles enter a finite-state system and move according to independent sample paths from a semi-Markov process. Strong limit theorems are developed for the ratio of the flow of particles from states i to j and the flow out of When the cumulative arrival of particles into the system up to time t, A (t) ∼ λtα, then a.s. When A (t)∼ λekt, then the flow between states must be normalized by the Laplace–Stieltjes transform of the conditional holding time distribution, in order to make the ratio an unbiased estimator of ρij.
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