ERROR BOUNDS FOR AUGMENTED TRUNCATIONS OF DISCRETE-TIME BLOCK-MONOTONE MARKOV CHAINS UNDER GEOMETRIC DRIFT CONDITIONS

作者：Masuyama Hiroyuki^*

来源：Advances in Applied Probability, 2015, 47(1): 83-105.

DOI：10.1017/s0001867800007710

• Augmented truncation
• block monotonicity
• blockwise dominance
• pathwise ordering
• geometric drift condition
• level-dependent QBD
• M/G/1-type Markov chain
• GI/M/1-type Markov chain
• GI/G/1-type Markov chain

In this paper we study the augmented truncation of discrete-time block-monotone Markov chains under geometric drift conditions. We first present a bound for the total variation distance between the stationary distributions of an original Markov chain and its augmented truncation. We also obtain such error bounds for more general cases, where an original Markov chain itself is not necessarily block monotone but is blockwise dominated by a block-monotone Markov chain. Finally, we discuss the application of our results to GI/G/1-type Markov chains.

• 出版日期2015-3