Vitali-type theorems for filter convergence related to vector lattice-valued modulars and applications to stochastic processes

Abstract

A Vitali-type theorem for vector lattice-valued modulars with respect to filter convergence is proved. Some applications are given to modular convergence theorems for moment operatorsin the vector lattice setting, and also for the Brownian motion and related stochastic processes.Comment: 19 pages, 2 figure