Randomly Weighted Sums of Conditionnally Dependent Random Variables

In this paper we study the asymptotic behavior for the tail probability of the randomly weighted sums and their maximum where the usual assumption of independence of random variable X and indepedence between the variable X and the weighted θ are relaxed. We suppose that, the variable X follows a conditional dependence intoduced by Geluk and Tang [6] and the pair (X, θ) follows a certain dependence structure proposed by Asimit and Badescu [1]. This result appears as a direct extension of the results of [7], [11] and [10].