Vector measures of bounded gamma-variation and stochastic integrals

TL;DR

This paper introduces vector measures of bounded gamma-variation and explores their connection to stochastic integrals with respect to Brownian motion, advancing the understanding of vector-valued stochastic calculus.

Contribution

It presents a new class of vector measures of bounded gamma-variation and analyzes their relationship with stochastic integrals, providing novel insights into vector-valued stochastic analysis.

Findings

Defined the class of vector measures of bounded gamma-variation

Established relationships between these measures and stochastic integrals

Enhanced understanding of vector-valued stochastic calculus

Abstract

We introduce the class of vector measures of bounded $\gamma$-variation and study its relationship with vector-valued stochastic integrals with respect to Brownian motions.