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arXiv · 1205.6976

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

Krzysztof Paczka
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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.

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Krzysztof Paczka. 2012-11-27. Doob's optional sampling and maximal inequality for $G$-martingales. https://arxiv.org/abs/1205.6976

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