TY - JOUR
T1 - Two-sided bounds for Lp-norms of combinations of products of independent random variables
AU - Damek, Ewa
AU - Latała, Rafał
AU - Nayar, Piotr
AU - Tkocz, Tomasz
PY - 2015
Y1 - 2015
N2 - We show that for every positive p, the Lp-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 lp-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 Lp-moments of partial sums of perpetuities.
AB - We show that for every positive p, the Lp-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 lp-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 Lp-moments of partial sums of perpetuities.
KW - Estimation of moments
KW - Perpetuity
KW - Product of independent random variables
KW - Riesz product
KW - Stochastic difference equation
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U2 - 10.1016/j.spa.2014.11.012
DO - 10.1016/j.spa.2014.11.012
M3 - Article
SN - 0304-4149
VL - 125
SP - 1688
EP - 1713
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
IS - 4
ER -