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On the first passage time of a simple random walk on a tree

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  • Bapat, R.B.

Abstract

We consider a simple random walk on a tree. Exact expressions are obtained for the expectation and the variance of the first passage time, thereby recovering the known result that these are integers. A relationship of the mean first passage matrix with the distance matrix is established and used to derive a formula for the inverse of the mean first passage matrix.

Suggested Citation

  • Bapat, R.B., 2011. "On the first passage time of a simple random walk on a tree," Statistics & Probability Letters, Elsevier, vol. 81(10), pages 1552-1558, October.
  • Handle: RePEc:eee:stapro:v:81:y:2011:i:10:p:1552-1558
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    References listed on IDEAS

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    1. Palacios, JoséLuis & Tetali, Prasad, 1996. "A note on expected hitting times for birth and death chains," Statistics & Probability Letters, Elsevier, vol. 30(2), pages 119-125, October.
    2. Chen, Haiyan, 2007. "The generating functions of hitting times for random walk on trees," Statistics & Probability Letters, Elsevier, vol. 77(15), pages 1574-1579, September.
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    Cited by:

    1. Palacios, José Luis & Renom, José M., 2012. "On partial sums of hitting times," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 783-785.

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