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

  • Dindiene, Lina ;
  • Leipus, Remigijus ;
  • Siaulys, Jonas
  • Received : 2016.11.25
  • Accepted : 2017.06.19
  • Published : 2017.11.01

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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