Average case behavior of random search for the maximum

Document Type

Article

Publication Date

1-1-1997

Abstract

This paper is a study of the error in approximating the global maximum of a Brownian motion on the unit interval by observing the value at randomly chosen points. One point of view is to look at the error from random sampling for a given fixed Brownian sample path; another is to look at the error with both the path and observations random. In the first case we show that for almost all Brownian paths the error, normalized by multiplying by the square root of the number of observations, does not converge in distribution, while in the second case the normalized error does converge in distribution. We derive the limiting distribution of the normalized error averaged over all paths.

Identifier

0031220885 (Scopus)

Publication Title

Journal of Applied Probability

External Full Text Location

https://doi.org/10.1017/S0021900200101305

ISSN

00219002

First Page

632

Last Page

642

Issue

3

Volume

34

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