Two-sided bounds for $L_p$-norms of combinations of products of independent random variables

Ewa Damek; Rafał Latała; Piotr Nayar; Tomasz Tkocz

doi:10.1016/j.spa.2014.11.012

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arXiv · 1404.0344

Two-sided bounds for $L_p$-norms of combinations of products of independent random variables

Ewa Damek·Rafał Latała·Piotr Nayar·Tomasz Tkocz

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Abstract

We show that for every positive p, the L_p-norm of linear combinations (with scalar or vector coefficients) of products of i.i.d. random variables, whose moduli have a nondegenerate distribution with the p-norm one, is comparable to the l_p-norm of the coefficients and the constants are explicit. As a result the same holds for linear combinations of Riesz products. We also establish the upper and lower bounds of the L_p-moments of partial sums of perpetuities.

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Ewa Damek, Rafał Latała, Piotr Nayar, Tomasz Tkocz. 2015-01-04. Two-sided bounds for $L_p$-norms of combinations of products of independent random variables. https://doi.org/10.1016/j.spa.2014.11.012

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