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Perturbed Markov Chains with Damping Component

Author

Listed:
  • Dmitrii Silvestrov

    (Stockholm University)

  • Sergei Silvestrov

    (Mälardalen University)

  • Benard Abola

    (Mälardalen University)

  • Pitos Seleka Biganda

    (Mälardalen University
    University of Dar es Salaam)

  • Christopher Engström

    (Mälardalen University)

  • John Magero Mango

    (Makerere University)

  • Godwin Kakuba

    (Makerere University)

Abstract

The paper is devoted to studies of regularly and singularly perturbed Markov chains with damping component. In such models, a matrix of transition probabilities is regularised by adding a special damping matrix multiplied by a small damping (perturbation) parameter ε. We perform a detailed perturbation analysis for such Markov chains, particularly, give effective upper bounds for the rate of approximation for stationary distributions of unperturbed Markov chains by stationary distributions of perturbed Markov chains with regularised matrices of transition probabilities, asymptotic expansions for approximating stationary distributions with respect to damping parameter, explicit coupling type upper bounds for the rate of convergence in ergodic theorems for n-step transition probabilities, as well as ergodic theorems in triangular array mode.

Suggested Citation

  • Dmitrii Silvestrov & Sergei Silvestrov & Benard Abola & Pitos Seleka Biganda & Christopher Engström & John Magero Mango & Godwin Kakuba, 2021. "Perturbed Markov Chains with Damping Component," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 369-397, March.
    • Handle: RePEc:spr:metcap:v:23:y:2021:i:1:d:10.1007_s11009-020-09815-9
    DOI: 10.1007/s11009-020-09815-9
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    References listed on IDEAS

    as
    1. Konstantin Avrachenkov & Alexey Piunovskiy & Yi Zhang, 2018. "Hitting Times in Markov Chains with Restart and their Application to Network Centrality," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1173-1188, December.
    2. Gyllenberg, Mats & Silvestrov, Dmitrii S., 2000. "Nonlinearly perturbed regenerative processes and pseudo-stationary phenomena for stochastic systems," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 1-27, March.
    Full references (including those not matched with items on IDEAS)

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