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Estimation of transition probabilities in a multiparticle semi-Markov system
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- Journal:
- Journal of Applied Probability / Volume 13 / Issue 4 / December 1976
- Published online by Cambridge University Press:
- 14 July 2016, pp. 696-706
- Print publication:
- December 1976
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- Article
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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.
When the cumulative arrival of particles into the system up to time 
a.s. When 
the Laplace–Stieltjes transform of the conditional holding time distribution, in order to make the ratio an unbiased estimator of 