Closure property and maximum of randomly weighted sums with heavy-tailed increments

2014 ◽  
Vol 91 ◽  
pp. 162-170 ◽  
Author(s):  
Yang Yang ◽  
Remigijus Leipus ◽  
Jonas Šiaulys
Keyword(s):  
Closure Property ◽  
Weighted Sums ◽  
Randomly Weighted Sums ◽  
Heavy Tailed

A note on the max-sum equivalence of randomly weighted sums of heavy-tailed random variables

2013 ◽  
Vol 18 (4) ◽  
pp. 519-525 ◽  
Author(s):  
Yang Yang ◽  
Kaiyong Wang ◽  
Remigijus Leipus ◽  
Jonas Šiaulys
Keyword(s):  
Random Variables ◽  
Tail Probability ◽  
Weighted Sums ◽  
Asymptotic Formulas ◽  
Dependence Structure ◽  
Insurance Risk ◽  
Risk Models ◽  
Randomly Weighted Sums ◽  
Random Weights ◽  
Heavy Tailed

This paper investigates the asymptotic behavior for the tail probability of the randomly weighted sums ∑k=1nθkXk and their maximum, where the random variables Xk and the random weights θk follow a certain dependence structure proposed by Asimit and Badescu [1] and Li et al. [2]. The obtained results can be used to obtain asymptotic formulas for ruin probability in the insurance risk models with discounted factors.

scholarly journals On The Complete Convergence Of Randomly Weighted Sums Of Random Fields

2014 ◽  
Vol 47 (1) ◽  
Author(s):  
Agnieszka M. Gdula ◽  
Andrzej Krajka
Keyword(s):  
Random Fields ◽  
Complete Convergence ◽  
Weighted Sums ◽  
Randomly Weighted Sums

AbstractLet {Xis convergent for some real t, some fixed p > 0 and all ε > 0. Here |n̲| is used for ΠThe randomly indexed sums of field {X

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