Mathematics – Probability
Scientific paper
2011-10-20
Stochastic Models, vol. 26, no. 4, pp. 505-548, 2010
Mathematics
Probability
This is a revised version of the paper published in Stochastic Models vol. 26, no. 4, pp. 505-548, 2010
Scientific paper
10.1080/15326349.2010.519661
This paper studies the light-tailed asymptotics of the stationary tail probability vectors of a Markov chain of M/G/1 type. Almost all related studies have focused on the typical case, where the transition block matrices in the non-boundary levels have a dominant impact on the decay rate of the stationary tail probability vectors and their decay is aperiodic. In this paper, we study not only the typical case but also atypical cases such that the stationary tail probability vectors decay periodically and/or their decay rate is determined by the tail distribution of jump sizes from the boundary level. We derive light-tailed asymptotic formulae for the stationary tail probability vectors by locating the dominant poles of the generating function of the sequence of those vectors. Further we discuss the positivity of the dominant terms of the obtained asymptotic formulae.
Daikoku Kentaro
Kimura Tatsuaki
Masuyama Hiroyuki
Takahashi Yutaka
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