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Paper detail

A subgeometric convergence formula for finite-level M/G/1-type Markov chains: via a block-decomposition-friendly solution for the Poisson equation of deviation matrix

This paper studies the subgeometric convergence of the stationary distribution in taking the infinite-level limit of a finite-level M/G/1-type Markov chain, that is, in letting the upper boundary level go to infinity. This study is performed through the fundamental deviation matrix, which is a block-decomposition-friendly solution for the Poisson equation of the deviation matrix. The fundamental deviation matrix yields a difference formula for the respective stationary distributions of the finite-level chain and the corresponding infinite-level chain. The difference formula plays a crucial role in deriving the main result of this paper: a subgeometric convergence formula for the infinite-level limit of the stationary distribution of the finite-level chain.

preprint2022arXivOpen access
Hiroyuki MasuyamaYosuke KatsumataTatsuaki Kimura
math.PR
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Hiroyuki MasuyamaYosuke KatsumataTatsuaki Kimura

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