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The moments of the random variable for the number of returns of a simple random walk

Published online by Cambridge University Press:  01 July 2016

Adrienne W. Kemp*
Affiliation:
University of St Andrews
*
Postal address: Department of Statistics, The North Haugh, University of St Andrews, St Andrews KY16 9SS, Scotland.
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Abstract

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The number of returns to the origin for a simple random walk starting and ending at the origin is reconsidered; closed-form expressions in μ are given for μ3 and μ4.

Type
Letters to the Editor
Copyright
Copyright © Applied Probability Trust 1987 

References

Dwass, M. (1967) Simple random walk and rank order statistics. Ann. Math. Statist. 38, 10421053.Google Scholar
Katzenbeisser, W. and Hackl, P. (1986) An alternative to the Kolmogorov-Smirnov two-sample test. Commun. Statist. Theory Methods 15, 11631177.Google Scholar
Katzenbeisser, W. and Panny, W. (1986) A note on the higher moments of the random variable T associated with the number of returns of a simple random walk. Adv. Appl. Prob. 18, 279282.Google Scholar
Kemp, A. W. (1968) A wide class of discrete distributions and the associated differential equations. Sankhya A 30, 401410.Google Scholar
Mcgilchrist, C. A. and Woodyer, K. D. (1975) Note on a distribution-free CUSUM technique. Technometrics 17, 321325.Google Scholar
Panny, W. (1984) The maximal deviation of lattice paths. Mathematical Systems in Economics Vol. 91. Verlagsgruppe Athenäum/Hain/Hanstein, Königstein/Ts.Google Scholar