Subexponential Asymptotics of the Stationary Distributions of GI/G/1-Type Markov Chains
Subexponential Asymptotics of the Stationary Distributions of GI/G/1-Type Markov Chains
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DOI：
10.1080/15326349.2013.783286
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发表时间：
2013-04
影响因子：
0.7
通讯作者：
Tatsuaki Kimura;H. Masuyama;Yutaka Takahashi
中科院分区：
文献类型：
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作者：
Tatsuaki Kimura;H. Masuyama;Yutaka Takahashi
本文研究了GI/G/1型马氏链在两种情况下平稳分布的次指数渐近性：（i）非边界层上的相变矩阵是随机的;（ii）它是严格次随机的.对于情形（i），我们给出了一个比文献中给出的更弱的次指数渐近的充分条件。至于情况（ii），次指数渐近性尚未研究，据我们所知。我们证明了情形（ii）的次指数渐近性不同于情形（i）。我们还研究了平稳分布在两种情况下的局部次指数渐近性（i）和（ii）。
This article 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 case (i), we present a weaker sufficient condition for the subexponential asymptotics than those given in the literature. As for case (ii), the subexponential asymptotics has not been studied, as far as we know. We show that the subexponential asymptotics in case (ii) is different from that in case (i). We also study the locally subexponential asymptotics of the stationary distributions in both cases (i) and (ii).