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Expected number of excursions above curved boundarie by a random walk

Published online by Cambridge University Press:  17 April 2009

Fima C. Klebaner
Fima C. Klebaner
Affiliation:
Department of StatisticsThe University of MelbourneParkville Vic 3052Australia
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Abstract

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An asymptotic relation for the expected number of excursions above a boundary g(n) by a random walk Sn, n = 1,2, ‥, N is given in terms of an integral involving g. An integral test is given to determine whether the total excursion time has finite expectation. If some moment assumptions hold then the expectation of the total excursions is finite if and only if .

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 41 , Issue 2 , April 1990 , pp. 207 - 213
Copyright
Copyright © Australian Mathematical Society 1990

References

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