Doob's optional sampling and maximal inequality for $G$-martingales

Abstract

The paper considers the martingale theory in the $G$-framework. A form of Doob's optional sampling is established, which allows to prove the exact analogue of the classical maximal inequality. The obtained results are used to improve the existing $G$-martingale representation theorems.

This paper has been withdrawn due to error in Theorem 7

References in corpus (3)

• G-Brownian Motion and Dynamic Risk Measure under Volatility Uncertainty
• Sublinear Expectations and Martingales in discrete time
• Uniqueness of the representation for $G$-martingales with finite variation