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Confidence bands for Brownian motion and applications to Monte Carlo simulation

Kendall, W.S.; Marin, Jean-Michel; Robert, Christian P. (2007), Confidence bands for Brownian motion and applications to Monte Carlo simulation, Statistics and Computing, 17, 1, p. 1-10. http://dx.doi.org/10.1007/s11222-006-9001-z

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Type
Article accepté pour publication ou publié
Date
2007
Journal name
Statistics and Computing
Volume
17
Number
1
Publisher
Springer
Pages
1-10
Publication identifier
Metadata
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Author(s)
Kendall, W.S.
Marin, Jean-Michel cc
Robert, Christian P.
Abstract (EN)
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.
Subjects / Keywords
Boundary crossing probability; Brownian motion; Central limit theorem; CUSUM; Local time; Monte Carlo path; Simultaneous confidence region