LEVEL-WISE SUBGEOMETRIC CONVERGENCE OF THE LEVEL-INCREMENT TRUNCATION APPROXIMATION OF M/G/1-TYPE MARKOV CHAINS

抄録

This paper considers the level-increment (LI) truncation approximation of M/G/1-type Markov chains. The LI truncation approximation is often used in implementing Ramaswami's recursion for computing the stationary distribution. We show that if the equilibrium level-increment distribution (in steady state) is long-tailed then its tail decay speed is asymptotically equal to the convergence speed of the level-wise difference between the original stationary distribution and its LI truncation approximation. We also show that the total variation norm of the relative level-wise (not whole) difference of the original stationary distribution and its LI truncation approximation is asymptotically independent of the level.