turkmath.org

Let $( X_1, X_2, \ldots )$ be a sequence of pairwise asymptotically independent and real-valued random variables, and$ ( \Theta_1, \Theta_2, \ldots )$ be another sequence of nonnegative and nondegenerate at zero r.v.s., independent of $( X_1, X_2, \ldots )$. In this paper, we investigate the tail behavior of randomly weighted infinite sums under the assumption that $( S_\infty^+ = \sum_{n=1}^{\infty} = \Theta_n X_n^+ )$ (where $( X_n^+ = \max\{X_n , 0\} ) )$ has a consistently varying tail, as well as some moment conditions on $( \Theta_1, \Theta_2, \ldots )$. Our obtained result is more easily verifiable than some existing ones restricting the conditions on $( X_1, X_2, \ldots )$.