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The higher moments of the number of returns of a simple random walk

Published online by Cambridge University Press:  01 July 2016

Peter Kirschenhofer  and
Helmut Prodinger
Peter Kirschenhofer*
Affiliation:
Technical University of Vienna
Helmut Prodinger*
Affiliation:
Technical University of Vienna
*
* Postal address: Department of Algebra and Discrete Mathematics, Wiedner Hauptstr. 8–10/118, Technical University of Vienna, A-1040 Wien, Austria.
* Postal address: Department of Algebra and Discrete Mathematics, Wiedner Hauptstr. 8–10/118, Technical University of Vienna, A-1040 Wien, Austria.
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Abstract

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We consider a simple random walk starting at 0 and leading to 0 after 2n steps. By a generating functions approach we achieve closed formulae for the moments of the random variables ‘number of visits to the origin'.

Keywords

GENERATING FUNCTIONSCATALAN NUMBERS
Type
Letter to the Editor
Information
Advances in Applied Probability , Volume 26 , Issue 2 , June 1994 , pp. 561 - 563
Copyright
Copyright © Applied Probability Trust 1994 

References

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