Caracterisation de processus a trajectoires majorees ou continues

Abstract

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Necessary and sufficient conditions for Hölder continuity of Gaussian processes

“…The differences between the classical Kolmogorov-Čentsov continuity criterion and Theorem 1 are: (i) Theorem 1 deals only with Gaussian processes, (ii) there is an ε-gap to the classical Kolmogorov-Čentsov condition and (iii) as a bonus we obtain that the Hölder constants C ε must have light tails by the estimate (6). Note that the ε-gap cannot be closed.…”

Majorizing measures on metric spaces

“…Such a property (see Talagrand [8]) is equivalent to the following condition: where the supremum is taken over all processes that satisfy (1). We recall (see Fernique [3]) that a Borel probability measure…”

The majorizing measure approach to sample boundedness

“…. A simple chaining argument shows (see [8]) that the existence of a majorizing measure suffices for sample boundedness of X(t), t ∈ T .…”