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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… Click to show full 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.
Journal Title: Lithuanian Mathematical Journal
Year Published: 2019
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