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Investigation of some probabilistic characteristics of one class of semi-Markov wandering with delaying screens

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Abstract

The process of semi-Markov wandering with delaying screens “b” and “a” (a > b > 0) is constructed by the given sequence of independent and identically distributed random vectors (ξ i , η i ), i ≥ 1. The integral equation for the Laplace transform by time and the Laplace-Stieltjes transform by the phase of its conditional distribution is derived. If the wandering occurs by a complicated Laplace distribution, the ergodic distribution of the process and its moments are found. Then, the integral equation for the generating function of the conditional distribution of the number of process steps at which it firstly reaches the level a is derived. When the wandering occurs by the simple Laplace distribution, its generating functions and moments are found.

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Authors and Affiliations

  1. Baku State University, ul. Z. Khalilova 23, Baku, AZ, 1148, Azerbaijan

    T. I. Nasirova & B. G. Shamilova

Authors
  1. T. I. Nasirova
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  2. B. G. Shamilova
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Corresponding author

Correspondence to T. I. Nasirova.

Additional information

Original Russian Text © T.I. Nasirova, B.G. Shamilova, 2014, published in Avtomatika i Vychislitel’naya Tekhnika, 2014, No. 2, pp. 64–75.

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Nasirova, T.I., Shamilova, B.G. Investigation of some probabilistic characteristics of one class of semi-Markov wandering with delaying screens. Aut. Control Comp. Sci. 48, 109–119 (2014). https://doi.org/10.3103/S0146411614020059

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  • DOI: https://doi.org/10.3103/S0146411614020059

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