On the arg max of a Gaussian process

It is shown that if {Xt: t [set membership, variant] T} is a Gaussian process such that (T, [varrho]) is a separable metric space, where [varrho](t, s) = Cov(Xt,Xs), then, with probability 1, no sample path of X can achieve its supremum at two distinct points of T. Conversely if Pr* {supt[set membership, variant]TXt < [infinity]}>0 then (T, [varrho]) is a separable pseudometric space.

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Year of publication:	1992
Authors:	Arcones, Miguel A.
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 15.1992, 5, p. 373-374
Publisher:	Elsevier

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005138263