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

2012/05/31 by Krzysztof Paczka, Paczka, Krzysztof
Economics, Econometrics and Finance · Mathematics · #60G05 #60G44 #60G48 #Advanced Harmonic Analysis Research #FOS: Mathematics #Mathematical Analysis and Transform Methods #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1205.6976

openalex publication_date 2012/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• G-Brownian Motion and Dynamic Risk Measure under Volatility Uncertainty
• Uniqueness of the representation for G-martingales with finite variation

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