Subexponential asymptotics of the stationary distributions of M/G/1-type Markov chains

This paper studies the subexponential asymptotics of the stationary distribution of an M/G/1-type Markov chain. We provide a sufficient condition for the subexponentiality of the stationary distribution. The sufficient condition requires only the subexponential integrated tail of level increments. On the other hand, the previous studies assume the subexponentiality of level increments themselves and/or the aperiodicity of the G-matrix. Therefore, our sufficient condition is weaker than the existing ones. We also mention some errors in the literature.

► We study the subexponential tail asymptotics of M/G/1-type Markov chains. ► We show a sufficient condition for the subexponential stationary distribution. ► Our sufficient condition is weaker than those in the previous studies. ► We also mention some errors in the literature.