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arXiv · 1607.03619

Randomly stopped sums with consistently varying distributions

Edita Kizinevič·Jonas Sprindys·Jonas Šiaulys
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Abstract

Let $\{ξ_1,ξ_2,\ldots\}$ be a sequence of independent random variables, and $η$ be a counting random variable independent of this sequence. We consider conditions for $\{ξ_1,ξ_2,\ldots\}$ and $η$ under which the distribution function of the random sum $S_η=ξ_1+ξ_2+\cdots+ξ_η$ belongs to the class of consistently varying distributions. In our consideration, the random variables $\{ξ_1,ξ_2,\ldots\}$ are not necessarily identically distributed.

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Edita Kizinevič, Jonas Sprindys, Jonas Šiaulys. 2016-07-13. Randomly stopped sums with consistently varying distributions. https://doi.org/10.15559/16-vmsta60

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