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.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2012
- DOI:
- 10.48550/arXiv.1205.6976
- arXiv:
- arXiv:1205.6976
- Bibcode:
- 2012arXiv1205.6976P
- Keywords:
-
- Mathematics - Probability;
- 60G05;
- 60G44;
- 60G48
- E-Print:
- This paper has been withdrawn due to error in Theorem 7