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

Kiyoshi Inoue (), Sigeo Aki and Balakrishnan Narayanaswamy
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Kiyoshi Inoue: Seikei University
Sigeo Aki: Kansai University
Balakrishnan Narayanaswamy: McMaster University

Methodology and Computing in Applied Probability, 2013, vol. 15, issue 2, 349-362

Abstract: 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.

Keywords: Random walk; Number of visits; Waiting time; Cover times; Hitting times; Graph; Tree; Expected value; Probability generating function; Double generating function; Primary 60J10, 62E15; Secondary 60C05, 60E05 (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11009-011-9246-7

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