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On the number of times where a simple random walk reaches its maximum

Part of: Approximations and expansions Nonparametric inference

Published online by Cambridge University Press:  14 July 2016

W. Katzenbeisser  and
W. Panny
W. Katzenbeisser*
Affiliation:
University of Economics, Vienna
W. Panny*
Affiliation:
University of Economics, Vienna
*
∗Postal address: Department of Statistics, University of Economics, Augasse 2-6, A-1090 Vienna, Austria.
∗∗Postal address: Department of Computer Science, University of Economics, Augasse 2-6, A-1090 Vienna, Austria.
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Abstract

Let Qn denote the number of times where a simple random walk reaches its maximum, where the random walk starts at the origin and returns to the origin after 2n steps. Such random walks play an important role in probability and statistics. In this paper the distribution and the moments of Qn, are considered and their asymptotic behavior is studied.

Keywords

LATTICE PATHSRANK-ORDER STATISTICSKOLMOGOROV–SMIRNOV TESTASYMPTOTIC EXPANSIONS

MSC classification

Secondary: 62G30: Order statistics; empirical distribution functions 41A60: Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 29 , Issue 2 , June 1992 , pp. 305 - 312
Copyright
Copyright © Applied Probability Trust 1992 

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References

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