The majorizing measure approach to sample boundedness

Witold Bednorz¹

¹ Institute of Mathematics University of Warsaw Banacha 2 02-097 Warszawa, Poland

Colloquium Mathematicum, Tome 139 (2015) no. 2, pp. 205-227

Résumé

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.

Détail

DOI : 10.4064/cm139-2-4

Keywords: describe alternative approach sample boundedness continuity stochastic processes regularity paths understood terms distribution argument maximum centered gaussian process obtain short proof exact lower bound mathbb sup finally prove equivalence usual majorizing measure functional its conjugate version