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Approximation Formulas for the Ergodic Moments of Gaussian Random Walk with a Reflecting Barrier

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Advances in Applied Mathematics and Approximation Theory

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 41))

Abstract

In this study, Gaussian random walk process with a generalized reflecting barrier is constructed mathematically. Under some weak conditions, the ergodicity of the process is discussed and exact form of the first four moments of the ergodic distribution is obtained. After, the asymptotic expansions for these moments are established. Moreover, the coefficients of the asymptotic expansions are expressed by means of numerical characteristics of a residual waiting time.

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Acknowledgements

This study was partially supported by TUBITAK (110T559 coded project).

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Authors and Affiliations

  1. TOBB University of Economics and Technology, Ankara, Turkey

    Tahir Khaniyev & Basak Gever

  2. Karadeniz Technical University, Trabzon, Turkey

    Zulfiyya Mammadova

Authors
  1. Tahir Khaniyev
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  2. Basak Gever
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  3. Zulfiyya Mammadova
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Corresponding author

Correspondence to Basak Gever .

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Editors and Affiliations

  1. , Department of Mathematical Sciences, The University of Memphis, Memphis, 38152, Tennessee, USA

    George A. Anastassiou

  2. , Department of Mathematics, TOBB Economics and Technology University, Sögütözü, Ankara, 06530, Turkey

    Oktay Duman

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Khaniyev, T., Gever, B., Mammadova, Z. (2013). Approximation Formulas for the Ergodic Moments of Gaussian Random Walk with a Reflecting Barrier. In: Anastassiou, G., Duman, O. (eds) Advances in Applied Mathematics and Approximation Theory. Springer Proceedings in Mathematics & Statistics, vol 41. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6393-1_13

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