Random convolution of inhomogeneous distributions with O-exponential tail

Modern Stochastics: Theory and Applications

Svetlana Danilenko¹  Simona Paškauskaitė²  Jonas Šiaulys² 

[1] Faculty of Fundamental Sciences, Vilnius Gediminas Technical University, Saulėtekio al. 11, Vilnius LT-10223, Lithuania;Faculty of Mathematics and Informatics, Vilnius University, Naugarduko 24, Vilnius LT-03225, Lithuania;

关键词: Heavy tail;    exponential tail;    O-exponential tail;    random sum;    random convolution;    inhomogeneous distributions;   

DOI  :  10.15559/16-VMSTA52

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown