Modern Stochastics: Theory and Applications

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Keywords: random convolution

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Random convolution of inhomogeneous distributions with

$O$ -exponential tail

Svetlana Danilenko Simona Paškauskaitė Jonas Šiaulys

https://doi.org/10.15559/16-VMSTA52

Pub. online: 4 Apr 2016 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 3, Issue 1 (2016), pp. 79–94

Abstract

Let

$\{\xi _{1},\xi _{2},\dots \}$ be a sequence of independent random variables (not necessarily identically distributed), and η be a counting random variable independent of this sequence. We obtain sufficient conditions on

$\{\xi _{1},\xi _{2},\dots \}$ and η under which the distribution function of the random sum

$S_{\eta }=\xi _{1}+\xi _{2}+\cdots +\xi _{\eta }$ belongs to the class of

$\mathcal{O}$ -exponential distributions.

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