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Markov chains in random environment with applications in queuing theory and machine learning

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  • Lovas, Attila
  • Rásonyi, Miklós

Abstract

We prove the existence of limiting distributions for a large class of Markov chains on a general state space in a random environment. We assume suitable versions of the standard drift and minorization conditions. In particular, the system dynamics should be contractive on the average with respect to the Lyapunov function and large enough small sets should exist with large enough minorization constants. We also establish that a law of large numbers holds for bounded functionals of the process. Applications to queuing systems, to machine learning algorithms and to autoregressive processes are presented.

Suggested Citation

  • Lovas, Attila & Rásonyi, Miklós, 2021. "Markov chains in random environment with applications in queuing theory and machine learning," Stochastic Processes and their Applications, Elsevier, vol. 137(C), pages 294-326.
    • Handle: RePEc:eee:spapps:v:137:y:2021:i:c:p:294-326
    DOI: 10.1016/j.spa.2021.04.002
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    References listed on IDEAS

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    1. Fabienne Comte & Eric Renault, 1998. "Long memory in continuous‐time stochastic volatility models," Mathematical Finance, Wiley Blackwell, vol. 8(4), pages 291-323, October.
    2. Burton, Robert M. & Dehling, Herold, 1990. "Large deviations for some weakly dependent random processes," Statistics & Probability Letters, Elsevier, vol. 9(5), pages 397-401, May.
    3. Jim Gatheral & Thibault Jaisson & Mathieu Rosenbaum, 2018. "Volatility is rough," Quantitative Finance, Taylor & Francis Journals, vol. 18(6), pages 933-949, June.
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    Cited by:

    1. Rásonyi, Miklós & Tikosi, Kinga, 2022. "On the stability of the stochastic gradient Langevin algorithm with dependent data stream," Statistics & Probability Letters, Elsevier, vol. 182(C).
    2. Valeriy Naumov & Konstantin Samouylov, 2021. "Resource System with Losses in a Random Environment," Mathematics, MDPI, vol. 9(21), pages 1-10, October.
    3. Balázs Gerencsér & Miklós Rásonyi, 2023. "On the Ergodicity of Certain Markov Chains in Random Environments," Journal of Theoretical Probability, Springer, vol. 36(4), pages 2093-2125, December.

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