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Explicit stationary distribution of the (L, 1)-reflecting random walk on the half line

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Abstract

In this paper, we consider the (L, 1) state-dependent reflecting random walk (RW) on the half line, which is an RW allowing jumps to the left at a maximal size L. For this model, we provide an explicit criterion for (positive) recurrence and an explicit expression for the stationary distribution. As an application, we prove the geometric tail asymptotic behavior of the stationary distribution under certain conditions. The main tool employed in the paper is the intrinsic branching structure within the (L, 1)-random walk.

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Authors and Affiliations

  1. School of Mathematical Sciences & Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing, 100875, P. R. China

    Wen Ming Hong & Ke Zhou

  2. School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada, K1S 5B6

    Yi Qiang & Q. Zhao

Authors
  1. Wen Ming Hong
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  2. Ke Zhou
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  3. Yi Qiang
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  4. Q. Zhao
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Corresponding author

Correspondence to Ke Zhou.

Additional information

Supported by National Natural Science Foundation of China (Grant No. 11131003) and the Natural Sciences and Engineering Research Council of Canada (Grant No. 315660)

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Hong, W.M., Zhou, K., Qiang, Y. et al. Explicit stationary distribution of the (L, 1)-reflecting random walk on the half line. Acta. Math. Sin.-English Ser. 30, 371–388 (2014). https://doi.org/10.1007/s10114-014-3009-7

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  • DOI: https://doi.org/10.1007/s10114-014-3009-7

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