Kendall, W. S., Marin, Jean-Michel and Robert, Christian P. (2007) Confidence bands for Brownian motion and applications to Monte Carlo simulation. Statistics and Computing, Vol.17 (No.1). pp. 1-10. doi:10.1007/s11222-006-9001-z

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Abstract

Minimal area regions are constructed for Brownian paths and perturbed Brownian paths. While the theoretical optimal region cannot be obtained in closed form, we provide practical confidence regions based on numerical approximations and local time arguments. These regions are used to provide informal convergence assessments for both Monte Carlo and Markov Chain Monte Carlo experiments, via the Brownian asymptotic approximation of cumulative sums.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Brownian motion processes, Confidence intervals, Monte Carlo method
Journal or Publication Title:	Statistics and Computing
Publisher:	Springer
ISSN:	0960-3174
Official Date:	March 2007
Dates:	Date Event March 2007 Published
Date of first compliant deposit:	9 December 2015
Volume:	Vol.17
Number:	No.1
Number of Pages:	10
Page Range:	pp. 1-10
DOI:	10.1007/s11222-006-9001-z
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access

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