On some limit theorems following from Smith's Theorem
Probability
2016-03-22 v2
Abstract
We give a generalization of the ergodic theorem for semi-Markov linear-type processes. This generalization is proved for the case when a common support of distributions defining this process is not arithmetic. Also we give an uniform estimate of expectations of the forward renewal time. These facts are based on the key renewal (Walter Smith's) theorem, and they are very useful in research in the queueing theory.
Cite
@article{arxiv.1509.06178,
title = {On some limit theorems following from Smith's Theorem},
author = {Galina A. Zverkina},
journal= {arXiv preprint arXiv:1509.06178},
year = {2016}
}
Comments
9 pages, in Russian. The second corrected version is in English; 13 pages