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Asymptotic expansions for the moments of a semi-Markovian random walk with exponential distributed interference of chance

Author

Listed:
  • Khaniyev, T.
  • Kesemen, T.
  • Aliyev, R.
  • Kokangul, A.

Abstract

In this paper, a semi-Markovian random walk process (X(t)) with a discrete interference of chance is constructed and the ergodicity of this process is discussed. Some exact formulas for the first- and second-order moments of the ergodic distribution of the process X(t) are obtained, when the random variable [zeta]1 has an exponential distribution with the parameter [lambda]>0. Here [zeta]1 expresses the quantity of a discrete interference of chance. Based on these results, the third-order asymptotic expansions for mathematical expectation and variance of the ergodic distribution of the process X(t) are derived, when [lambda]-->0.

Suggested Citation

  • Khaniyev, T. & Kesemen, T. & Aliyev, R. & Kokangul, A., 2008. "Asymptotic expansions for the moments of a semi-Markovian random walk with exponential distributed interference of chance," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 785-793, April.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:6:p:785-793
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    References listed on IDEAS

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    1. Tahir A. Khaniev & Halim Özdemir & Selahattin Maden, 1998. "Calculating the probability characteristics of a boundary functional of a semi‐continuous random process with reflecting and delaying screens," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 14(2), pages 117-123, June.
    2. Alsmeyer, Gerold, 1991. "Some relations between harmonic renewal measures and certain first passage times," Statistics & Probability Letters, Elsevier, vol. 12(1), pages 19-27, July.
    3. Khaniyev, Tahir & Kucuk, Zafer, 2004. "Asymptotic expansions for the moments of the Gaussian random walk with two barriers," Statistics & Probability Letters, Elsevier, vol. 69(1), pages 91-103, August.
    4. Brown, Mark & Solomon, Herbert, 1975. "A second-order approximation for the variance of a renewal reward process," Stochastic Processes and their Applications, Elsevier, vol. 3(3), pages 301-314, July.
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    1. Aliyev, Rovshan & Bayramov, Veli, 2017. "On the asymptotic behaviour of the covariance function of the rewards of a multivariate renewal–reward process," Statistics & Probability Letters, Elsevier, vol. 127(C), pages 138-149.

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