Institute of Mathematical Statistics Lecture Notes - Monograph Series

Random walk on a polygon

Jyotirmoy Sarka

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Abstract

A particle moves among the vertices of an $(m+1)$-gon which are labeled clockwise as $0, 1, \ldots, m$. The particle starts at $0$ and thereafter at each step it moves to the adjacent vertex, going clockwise with a known probability $p$, or counterclockwise with probability $1-p$. The directions of successive movements are independent. What is the expected number of moves needed to visit all vertices? This and other related questions are answered using recursive relations.

Chapter information

Source
Jiayang Sun, Anirban DasGupta, Vince Melfi, Connie Page, eds., Recent Developments in Nonparametric Inference and Probability: Festschrift for Michael Woodroofe (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2006), 31-43

Dates
First available in Project Euclid: 28 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.lnms/1196284051

Digital Object Identifier
doi:10.1214/074921706000000581

Subjects
Primary: 60G50: Sums of independent random variables; random walks
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]

Keywords
Gambler's ruin recursive relation conditional probability mathematical induction difference equation L'Hospital's rule Bayes' rule

Rights
Copyright © 2006, Institute of Mathematical Statistics

Citation

Sarka, Jyotirmoy. Random walk on a polygon. Recent Developments in Nonparametric Inference and Probability, 31--43, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2006. doi:10.1214/074921706000000581. https://projecteuclid.org/euclid.lnms/1196284051


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