A note on almost sure behavior of randomly weighted sums of φ-mixing random variables with φ-mixing weights

Abstract

Randomly weighted sums play an important role in various applied and theoretical problems, e.g., in actuarial mathematics or statistics. The almost sure convergence of randomly weighted sums is usually studied under the assumption that sequences are independent and identically distributed. In this note, we assume that both sequences are φ-mixing. Under some additional conditions, we prove a strong law of large numbers for sequences of randomly weighted sums.