ON THE EXISTENCE OF A SMALL PARAMETER FOR A SEMI-MARKOV PROCESS


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Abstract

The problem of existence of a small parameter for a decomposable semi-Markov process with a finite number of states E is investigated in the case where the phase space E of the process can be represented in the form of the union E=⋓{k=1}{r}E{k} of disjoint sets E{1},⋖,E{r} of ergodic states. The asymptotic behavior of transition probabilities of the semi-Markov process with phase space E=⋓{k=0}{r}E{k}, where E0 is the set of unessential states and Ek, k=1,⋖,r, are classes of ergodic states, is studied.

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