# CLOSURE PROPERTY AND TAIL PROBABILITY ASYMPTOTICS FOR RANDOMLY WEIGHTED SUMS OF DEPENDENT RANDOM VARIABLES WITH HEAVY TAILS

• Dindiene, Lina ;
• Leipus, Remigijus ;
• Siaulys, Jonas
• Accepted : 2017.06.19
• Published : 2017.11.01
• 23 2

#### Abstract

In this paper we study the closure property and probability tail asymptotics for randomly weighted sums $S^{\Theta}_n={\Theta}_1X_1+{\cdots}+{\Theta}_nX_n$ for long-tailed random variables $X_1,{\ldots},X_n$ and positive bounded random weights ${\Theta}_1,{\ldots},{\Theta}_n$ under similar dependence structure as in [26]. In particular, we study the case where the distribution of random vector ($X_1,{\ldots},X_n$) is generated by an absolutely continuous copula.

#### Keywords

randomly weighted sum;long-tail distribution;copula;FGM copula

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