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

Author

Listed:
  • Damek, Ewa
  • Latała, Rafał
  • Nayar, Piotr
  • Tkocz, Tomasz

Abstract

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.

Suggested Citation

  • Damek, Ewa & Latała, Rafał & Nayar, Piotr & Tkocz, Tomasz, 2015. "Two-sided bounds for Lp-norms of combinations of products of independent random variables," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1688-1713.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:4:p:1688-1713
    DOI: 10.1016/j.spa.2014.11.012
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    References listed on IDEAS

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    1. Collamore, Jeffrey F. & Vidyashankar, Anand N., 2013. "Tail estimates for stochastic fixed point equations via nonlinear renewal theory," Stochastic Processes and their Applications, Elsevier, vol. 123(9), pages 3378-3429.
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