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Subexponential Asymptotics of the Stationary Distributions of GI/G/1-Type Markov Chains
This paper considers the subexponential asymptotics of the stationary
distributions of GI/G/1-type Markov chains in two cases: (i) the phase
transition matrix in non-boundary levels is stochastic; and (ii) it is strictly
substochastic. For the case (i), we present a weaker sufficient condition for
the sub exponential asymptotics than those given in the literature. As for the
case (ii), the subexponential asymptotics has not been studied, as far as we
know. We show that the subexponential asymptotics in the case (ii) is different
from that in the case (i). We also study the locally subexponential asymptotics
of the stationary distributions in both cases (i) and (ii).Comment: This is a revised version of the paper published in Stochastic Models
vol. 29, no. 2, pp. 190--293, 201