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Confidence bands for Brownian motion and applications to Monte Carlo simulation
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Kendall, Wilfrid 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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Official URL: http://dx.doi.org/10.1007/s11222-006-9001-z
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: |
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| Volume: | Vol.17 | ||||
| Number: | No.1 | ||||
| Number of Pages: | 10 | ||||
| Page Range: | pp. 1-10 | ||||
| Identifier: | 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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