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Norms of sub-exponential random vectors

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  • Zajkowski, Krzysztof

Abstract

We discuss various forms of the Luxemburg norm in spaces of random vectors with coordinates belonging to the classical Orlicz spaces of exponential type. We prove equivalent relations between some kinds of these forms. We also show when the so-called uniform norm is majorized by norms of coordinates up to some constants. We give an application of other norm to study of chaos in random vectors with sub-exponential coordinates.

Suggested Citation

  • Zajkowski, Krzysztof, 2019. "Norms of sub-exponential random vectors," Statistics & Probability Letters, Elsevier, vol. 152(C), pages 147-152.
    • Handle: RePEc:eee:stapro:v:152:y:2019:i:c:p:147-152
    DOI: 10.1016/j.spl.2019.05.002
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    Cited by:

    1. Zajkowski, Krzysztof, 2020. "Bounds on tail probabilities for quadratic forms in dependent sub-gaussian random variables," Statistics & Probability Letters, Elsevier, vol. 167(C).

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