The majorizing measure approach to the sample boundedness

Abstract

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\in T we obtain a short proof of the exact lower bound on E\sup_{t\in T} X(t). Finally we prove the equivalence of a usual majorizing measure functional to its conjugate version.