Adaptive approximation of the minimum of Brownian motion

Document Type

Article

Publication Date

4-1-2017

Abstract

We study the error in approximating the minimum of a Brownian motion on the unit interval based on finitely many point evaluations. We construct an algorithm that adaptively chooses the points at which to evaluate the Brownian path. In contrast to the 1/2 convergence rate of optimal nonadaptive algorithms, the proposed adaptive algorithm converges at an arbitrarily high polynomial rate.

Identifier

85007549058 (Scopus)

Publication Title

Journal of Complexity

External Full Text Location

https://doi.org/10.1016/j.jco.2016.11.002

e-ISSN

10902708

ISSN

0885064X

First Page

17

Last Page

37

Volume

39

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