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Asymptotic expansions for the moments of the Gaussian random walk with two barriers

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  • Khaniyev, Tahir
  • Kucuk, Zafer

Abstract

In this study, the semi-Markovian random walk (X(t)) with a normal distribution of summands and two barriers in the levels 0 and [beta]>0 is considered. Moreover, under some weak assumptions the ergodicity of the process is discussed and the characteristic function of the ergodic distribution of the process X(t) is expressed by means of appropriating one of a boundary functional SN. Using this relation, the exact formulas for the first four moments of ergodic distribution are obtained and the asymptotic expansions are derived with three terms for the one's, as [beta]-->[infinity]. Finally, using the Monte Carlo experiments, the degree of accuracy of obtained approximate formulas to exact one's have been tested.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:69:y:2004:i:1:p:91-103
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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.
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    Cited by:

    1. 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.

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