On Talagrand's Admissible Net Approach to Majorizing Measures and Boundedness of Stochastic Processes

Volume 56 / 2008

Witold Bednorz 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.

Authors

  • Witold BednorzDepartment of Mathematics
    University of Warsaw
    Banacha 2
    02-097 Warszawa, Poland
    e-mail

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