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Generating Functions of Waiting Times and Numbers of Visits for Random Walks on Graphs

Author

Listed:
  • Kiyoshi Inoue

    (Seikei University)

  • Sigeo Aki

    (Kansai University)

  • Balakrishnan Narayanaswamy

    (McMaster University)

Abstract

In this paper, we consider some cover time problems for random walks on graphs in a wide class of waiting time problems. By using generating functions, we present a unified approach for the study of distributions associated with waiting times. In addition, the distributions of the numbers of visits for the random walks on the graphs are also studied. We present the relationship between the distributions of the waiting times and the numbers of visits. We also show that these theoretical results can be easily carried out through some computer algebra systems and present some numerical results for cover times in order to demonstrate the usefulness of the results developed. Finally, the study of cover time problems through generating functions leads to more extensive development.

Suggested Citation

  • Kiyoshi Inoue & Sigeo Aki & Balakrishnan Narayanaswamy, 2013. "Generating Functions of Waiting Times and Numbers of Visits for Random Walks on Graphs," Methodology and Computing in Applied Probability, Springer, vol. 15(2), pages 349-362, June.
    • Handle: RePEc:spr:metcap:v:15:y:2013:i:2:d:10.1007_s11009-011-9246-7
    DOI: 10.1007/s11009-011-9246-7
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    References listed on IDEAS

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    1. 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.
    2. Palacios, José Luis, 2009. "On hitting times of random walks on trees," Statistics & Probability Letters, Elsevier, vol. 79(2), pages 234-236, January.
    3. Palacios, José Luis & Renom, José Miguel & Berrizbeitia, Pedro, 1999. "Random walks on edge-transitive graphs (II)," Statistics & Probability Letters, Elsevier, vol. 43(1), pages 25-32, May.
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    Cited by:

    1. Kiyoshi Inoue & Sigeo Aki, 2014. "On sooner and later waiting time distributions associated with simple patterns in a sequence of bivariate trials," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(7), pages 895-920, October.

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