On the convergence of orthogonal series

Bednorz, Witold

doi:10.1016/j.crma.2011.02.001

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2015

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“…Note that in the case of Gaussian processes the above property was proved in [1], Theorem 4.2, yet also mentioned in [7] and known to Talagrand [15]. There are many cases (see [3,4,5]) where one can prove the lower bound on the supremum of stochastic processes in the form sup µ M(µ, µ). The benefit of the approach is that the lower bound has to be found for a given measure µ on T , which better fits the chaining argument.…”

Section: Theoremmentioning

confidence: 82%

The majorizing measure approach to sample boundedness

Bednorz

2015

Colloq. Math.

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In this paper we describe the alternative approach to the sample boundedness and continuity of stochastic processes. We show that the regularity of paths can be understood in terms of a distribution of the argument maximum. For a centered Gaussian process X(t), t ∈ T we obtain a short proof of the exact lower bound on E sup t∈T X(t). Finally we prove the equivalence of a usual majorizing measure functional to its conjugate version. * Subject classification: 60G15, 60G17 †

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