On the arg max of a Gaussian process

Miguel A. Arcones

Statistics & Probability Letters, 1992, vol. 15, issue 5, 373-374

Abstract: 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 0 then (T, [varrho]) is a separable pseudometric space.

Date: 1992
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