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Expected number of excursions above curved boundarie by a random walk
Published online by Cambridge University Press: 17 April 2009
Abstract
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 .
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- Copyright © Australian Mathematical Society 1990
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