Complete and complete moment convergence for randomly weighted sums of ρ*-mixing random variables and its applications

Abstract

ABSTRACTIn this paper, we will study the complete and complete moment convergence for double-indexed randomly weighted sums of -mixing random variables. Several sufficient conditions to prove the complete and complete moment convergence for randomly weighted sums of -mixing random variables are presented. The results obtained in this paper extend some corresponding ones in the literature. As applications, we further study the convergence of the state observers of linear-time-invariant systems and the complete consistency for the weighted estimator in nonparametric regression models based on -mixing random errors. Finally, some numerical simulations are provided to verify the validity of theoretical results.