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On the limiting behavior of the characteristic function of the ergodic distribution of the semi-Markov walk with two boundaries

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Abstract

The semi-Markov walk (X(t)) with two boundaries at the levels 0 and β > 0 is considered. The characteristic function of the ergodic distribution of the processX(t) is expressed in terms of the characteristics of the boundary functionals N(z) and S N(z), where N(z) is the firstmoment of exit of the random walk {Sn}, n ≥ 1, from the interval (−z, β − z), z ∈ [0, β]. The limiting behavior of the characteristic function of the ergodic distribution of the process W β (t) = 2X(t)/β − 1 as β → ∞ is studied for the case in which the components of the walk (η i) have a two-sided exponential distribution.

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Authors and Affiliations

  1. Baku State University, Baku, Azerbaijan

    R. T. Aliyev

  2. Guseynov Institute of Cybernetics, National Academy of Sciences, Baku, Azerbaijan

    R. T. Aliyev & T. A. Khaniyev

  3. ]TOBB Economy and Technology University, Ankara, Turkey

    T. A. Khaniyev

Authors
  1. R. T. Aliyev
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  2. T. A. Khaniyev
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Correspondence to R. T. Aliyev.

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Original Russian Text © R. T. Aliyev, T. A. Khaniyev, 2017, published in Matematicheskie Zametki, 2017, Vol. 102, No. 4, pp. 490–502.

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Aliyev, R.T., Khaniyev, T.A. On the limiting behavior of the characteristic function of the ergodic distribution of the semi-Markov walk with two boundaries. Math Notes 102, 444–454 (2017). https://doi.org/10.1134/S0001434617090164

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  • DOI: https://doi.org/10.1134/S0001434617090164

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