The majorizing measure approach to sample boundedness
Volume 139 / 2015
Colloquium Mathematicum 139 (2015), 205-227
MSC: Primary 60G15; Secondary 60G17.
DOI: 10.4064/cm139-2-4
Abstract
We describe an alternative approach to sample boundedness and continuity of stochastic processes. We show that the regularity of paths can be understood in terms of the 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 $\mathbb E \sup_{t\in T}X(t)$. Finally we prove the equivalence of the usual majorizing measure functional to its conjugate version.
