$L^p$ spaces in vector lattices and applications

TL;DR

This paper extends the theory of $L^p$ spaces to vector lattice-valued functions using filter convergence, and applies these results to classical inequalities and stochastic processes like Brownian Motion.

Contribution

It introduces $L^p$ spaces in vector lattices with filter convergence and applies them to inequalities and stochastic differential equations.

Findings

Classical inequalities extended to vector lattice context

Properties of Brownian Motion and Bridge analyzed

Applications to stochastic differential equations

Abstract

$L^p$ spaces are investigated for vector lattice-valued functions, with respect to filter convergence. As applications, some classical inequalities are extended to the vector lattice context, and some properties of the Brownian Motion and the Brownian Bridge are studied, to solve some stochastic differential equations.