Summary
It is shown that for all tangent sequences (d n) and (e n) of nonnegative or conditionally symmetric random variables and for every function Φ satisfying the growth condition Φ(2x)≦αΦ(x) the following inequality holds: \(E\Phi \left( {\mathop {\sup }\limits_n \left| {\sum\limits_{k = 1}^n {d_k } } \right|} \right) \leqq cE\Phi \left( {\mathop {\sup }\limits_n \left| {\sum\limits_{k = 1}^n {e_k } } \right|} \right)\). This generalizes results of J. Zinn and proves a conjecture of S. Kwapień and W.A. Woyczyński.
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Hitczenko, P. Comparison of moments for tangent sequences of random variables. Probab. Th. Rel. Fields 78, 223–230 (1988). https://doi.org/10.1007/BF00322019
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DOI: https://doi.org/10.1007/BF00322019