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3 Bulletin of the Polish Academy of Sciences. Mathematics

3 Bednorz W.

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Majorizing Measures and Ultrametric Spaces

Bednorz W.

Bulletin of the Polish Academy of Sciences. Mathematics

2012

Vol. 60, no 1

91--100

Talagrand's proof of the sufficiency of existence of a majorizing measure for the sample boundedness of processes with bounded increments used a contraction from a certain ultrametric space. We give a short proof of existence of such an ultrametric using admissible sequences of nets.

On Talagrand's admissible net approach to majorizing measures and boundedness of stochastic processes

Bednorz W.

Bulletin of the Polish Academy of Sciences. Mathematics

2008

Vol. 56, no 1

83-91

We show that the main result of [1] 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 [5]), and the second that the existence of a sequence of admissible nets is sufficient for sample boundedness of a stochastic process with bounded increments.

A note on the Men'shov-Rademacher inequality

Bednorz W.

Bulletin of the Polish Academy of Sciences. Mathematics

2006

Vol. 54, no 1

89-93

We improve the constants in the Men'shov-Rademacher inequality by showing that for n > 64, E[...) for all orthogonal random variables X1,..., Xn such that ∑[...]= 1.