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2 results

  • Perturbation analysis for continuous-time Markov chains in a weak sense

  • Part of
  • Na Lin, Yuanyuan Liu
  • Journal:
    Journal of Applied Probability / Volume 61 / Issue 4 / December 2024
    Published online by Cambridge University Press:
    13 May 2024, pp. 1278-1300
    Print publication:
    December 2024
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  • By the technique of augmented truncations, we obtain the perturbation bounds on the distance of the finite-time state distributions of two continuous-time Markov chains (CTMCs) in a type of weaker norm than the V-norm. We derive the estimates for strongly and exponentially ergodic CTMCs. In particular, we apply these results to get the bounds for CTMCs satisfying Doeblin or stochastically monotone conditions. Some examples are presented to illustrate the limitation of the V-norm in perturbation analysis and to show the quality of the weak norm.

  • Error Bounds for Augmented Truncations of Discrete-Time Block-Monotone Markov Chains under Geometric Drift Conditions

  • Part of
  • Hiroyuki Masuyama
  • Journal:
    Advances in Applied Probability / Volume 47 / Issue 1 / March 2015
    Published online by Cambridge University Press:
    04 January 2016, pp. 83-105
    Print publication:
    March 2015
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  • 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.