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On computations of limiting probability distributions of higher order Markov chains

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  • Xu, Jianhong

Abstract

In this paper, we further study a recent algorithm for computing the limiting probability distribution of a higher order Markov chain. We analyze the space complexity and flop count of the algorithm in comparison with another existing algorithm which relies on approximation to a stationary distribution. Then we recast the algorithm in a more general setting in which the higher order chain is regular yet its reduced first order chain may not be. We propose an easy way of ensuring the convergence of the algorithm. To address the downside of the algorithm’s slow convergence, we incorporate in it an existing extrapolation mechanism as a remedy, which renders an Accelerated Power Iteration (API) algorithm. This API algorithm appears to be highly effective as shown by numerical evidence.

Suggested Citation

  • Xu, Jianhong, 2026. "On computations of limiting probability distributions of higher order Markov chains," Applied Mathematics and Computation, Elsevier, vol. 531(C).
    • Handle: RePEc:eee:apmaco:v:531:y:2026:i:c:s0096300326002419
    DOI: 10.1016/j.amc.2026.130189
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