On Talagrand's Admissible Net Approach to Majorizing Measures and Boundedness of Stochastic Processes
Volume 56 / 2008
Bulletin Polish Acad. Sci. Math. 56 (2008), 83-91
MSC: 60G17, 28A99.
DOI: 10.4064/ba56-1-10
Abstract
We show that the main result of \cite{Bed1} on sufficiency of existence of a majorizing measure for boundedness of a stochastic process can be naturally split in two theorems, each of independent interest. The first is that the existence of a majorizing measure is sufficient for the existence of a sequence of admissible nets (as recently introduced by Talagrand \cite{Tal2}), and the second that the existence of a sequence of admissible nets is sufficient for sample boundedness of a stochastic process with bounded increments.
