Martingale transforms in vector lattices

Abstract

In this work, we extend our previous study [6] on martingale transforms in vector lattices by generalising the concept to include sub-sup transforms within this broader framework. We investigate refined conditions that ensure the order convergence of these transforms, viewed as a natural analogue of almost sure convergence in classical probability theory. Furthermore, we provide a concrete example illustrating the construction and properties of these transforms in the vector lattice setting.