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

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.

29 pages; main result stated in a more general form, minor typos corrected

References in corpus (3)

• The tail of the stationary distribution of a random coefficient AR(q) model
• Tail behavior of stationary solutions of random difference equations: the case of regular matrices
• $L_1$-norm of combinations of products of independent random variables

Cited by in corpus (1)

• Logarithmic tails of sums of products of positive random variables bounded by one