Decomposition of an $ L^{1}(T) $-bounded martingale and Applications in Riesz spaces

TL;DR

This paper presents a decomposition method for L^1(T)-bounded martingales within the framework of stochastic analysis in vector lattices, enabling new inequality results.

Contribution

It introduces a novel decomposition technique for martingales in vector lattices, expanding the theoretical foundation of stochastic analysis in this setting.

Findings

Decomposition of L^1(T)-bounded martingales into three components.

Applications to inequalities in stochastic analysis within vector lattices.

Enhanced understanding of martingale behavior in Riesz spaces.

Abstract

In this work, we give a decomposition of a martingale into three martingales with applications to certain types of inequalities in the new theory of Stochastic Analysis in Vector Lattices