Randomly stopped sums with consistently varying distributions

DOI10.15559/16-VMSTA60zbMATH Open1349.60083arXiv1607.03619OpenAlexW2472143408MaRDI QIDQ340828

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Publication date: 15 November 2016

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Abstract: Let $x{i}_1,x{i}_2,ldots$ be a sequence of independent random variables, and $eta$ be a counting random variable independent of this sequence. We consider conditions for $x{i}_1,x{i}_2,ldots$ and $eta$ under which the distribution function of the random sum $S_{eta}=x{i}_1+x{i}_2+cdots+x{i}_{eta}$ belongs to the class of consistently varying distributions. In our consideration, the random variables $x{i}_1,x{i}_2,ldots$ are not necessarily identically distributed.

Full work available at URL: https://arxiv.org/abs/1607.03619

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