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Search: MSC category 60G15 ( Gaussian processes )

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1. CJM 2008 (vol 60 pp. 313)

Choi, Yong-Kab; o, Miklós Csörg\H
Asymptotic Properties for Increments of $l^{\infty}$-Valued Gaussian Random Fields
This paper establishes general theorems which contain both moduli of continuity and large incremental results for $l^\infty$-valued Gaussian random fields indexed by a multidimensional parameter under explicit conditions.

Keywords:$l^\infty$-valued Gaussian random field, modulus of continuity, regularly varying function, large deviation probability
Categories:60F15, 60G15, 60G60

2. CJM 2002 (vol 54 pp. 533)

Castelle, Nathalie
Approximations fortes pour des processus bivariés
Nous \'etablissons un r\'esultat d'approximation forte pour des processus bivari\'es ayant une partie gaus\-sien\-ne et une partie empirique. Ce r\'esultat apporte un nouveau point de vue sur deux th\'eor\`emes hongrois bidimensionnels \'etablis pr\'ec\'edemment, concernant l'approximation par un processus de Kiefer d'un processus empirique uniforme unidimensionnel et l'approximation par un pont brownien bidimensionnel d'un processus empirique uniforme bidimensionnel. Nous les enrichissons un peu et montrons que sous leur nouvelle forme ils ne sont que deux \'enonc\'es d'un m\^eme r\'esultat. We establish a strong approximation result for bivariate processes containing a Gaussian part and an empirical part. This result leads to a new point of view on two Hungarian bidimensional theorems previously established, about the approximation of an unidimensional uniform empirical process by a Kiefer process and the approximation of a bidimensional uniform empirical process by a bidimensional Brownian bridge. We enrich them slightly and we prove that, under their new fashion, they are but two statements of the same result.

Categories:60F17, 60G15, 62G30

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