Maxima of asymptotically Gaussian random fields and moderate deviation approximations to boundary crossing probabilities of sums of random variables with multidimensional indices

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dc.creatorChan, Hock Peng
dc.creatorLai, Tze Leung
dc.date2004-12-21
dc.date2006-02-24
dc.date.accessioned2026-07-07T06:39:12Z
dc.date.available2026-07-07T06:39:12Z
dc.descriptionSeveral classical results on boundary crossing probabilities of Brownian motion and random walks are extended to asymptotically Gaussian random fields, which include sums of i.i.d. random variables with multidimensional indices, multivariate empirical processes, and scan statistics in change-point and signal detection as special cases. Some key ingredients in these extensions are moderate deviation approximations to marginal tail probabilities and weak convergence of the conditional distributions of certain ``clumps'' around high-level crossings. We also discuss how these results are related to the Poisson clumping heuristic and tube formulas of Gaussian random fields, and describe their applications to laws of the iterated logarithm in the form of the Kolmogorov--Erdős--Feller integral tests.
dc.descriptionPublished at http://dx.doi.org/10.1214/009117905000000378 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0412428
dc.identifierhttp://arxiv.org/abs/math/0412428
dc.identifierAnnals of Probability 2006, Vol. 34, No. 1, 80-121
dc.identifierdoi:10.1214/009117905000000378
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/100989
dc.subjectProbability
dc.subject60F10, 60G60 (Primary) 60F20, 60G15 (Secondary)
dc.titleMaxima of asymptotically Gaussian random fields and moderate deviation approximations to boundary crossing probabilities of sums of random variables with multidimensional indices
dc.typetext

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