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Tails of higher-order moments with dominatedly varying summands∗

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Abstract

Let ξ1, . . . , ξn be dependent real-valued random variables with dominatedly varying distribution functions. We investigate the asymptotic behavior of the tail-moment E\( \left({\left({S}_n^{\xi}\right)}^m{1}_{\left\{{S}_n^{\upxi}>x\right\}}\right) \), where m is a nonnegative integer, and \( {S}_n^{\xi }={\xi}_1+\dots +{\xi}_n \). We consider the dependence structure, similar to pairwise strongly quasiasymptotic independence among the random summands. We also study the case where each summand of \( {S}_n^{\xi } \) can be expressed as the product of two random variables.

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Authors and Affiliations

  1. Institute of Applied Mathematics, Vilnius University, Naugarduko str. 24, LT-03225, Vilnius, Lithuania

    Remigijus Leipus

  2. Institute of Mathematics, Vilnius University, Naugarduko str. 24, LT-03225, Vilnius, Lithuania

    Jonas Šiaulys &  IevaVareikaitė

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  1. Remigijus Leipus
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  2. Jonas Šiaulys
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  3. IevaVareikaitė
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Correspondence to Remigijus Leipus.

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*Authors of the paper are supported by grant No. S-MIP-17-72 from the Research Council of Lithuania.

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Leipus, R., Šiaulys, J. & IevaVareikaitė Tails of higher-order moments with dominatedly varying summands∗. Lith Math J 59, 389–407 (2019). https://doi.org/10.1007/s10986-019-09444-x

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  • DOI: https://doi.org/10.1007/s10986-019-09444-x

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