Representation of G-martingales as stochastic integrals with respect to the G-Brownian motion

TL;DR

This paper establishes a representation theorem for symmetric G-martingales as stochastic integrals with respect to G-Brownian motion, expanding stochastic calculus under sublinear expectations.

Contribution

It introduces a novel representation of G-martingales as stochastic integrals, extending the theory of stochastic calculus in sublinear expectation spaces.

Findings

Symmetric G-martingales can be represented as stochastic integrals with G-Brownian motion.

Extended stochastic calculus for G-martingales under sublinear expectations.

Provides foundational results for G-martingale representation theory.

Abstract

The objective of this paper is to derive a representation of symmetric G-martingales as stochastic integrals with respect to the G-Brownian motion. For this end, we first study some extensions of stochastic calculus with respect to G-martingales under the sublinear expectation spaces.