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The expected number of visits of a sequence of normal partial sums to each side of a boundary

Published online by Cambridge University Press:  14 July 2016

Moshe Pollar*
Affiliation:
The Hebrew University of Jerusalem

Abstract

Let be the sequence of partial sums of independent N(μ, 1) random variables. The boundary in the {(n, Sn)} plane which minimizes the expected number of times n that Sn will be below a boundary when μ = θ > 0 subject to a given expected number of visits that Sn will be above the same boundary when μ = 0 is shown to be linear and is also characterized. Similar results are shown for Brownian motion.

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 1978 

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