The application of multi-dimensional Jensen’s inequality for G-martingale

Abstract

Jensen’s inequalities play a key role in probability theory. In this paper, we aim to construct G-martingales by Jensen’s inequalities in the form of G-expectation, and extend the above results to the n-dimensional case.

Keywords:

• G-expectation
• G-martingale
• Jensen’s inequality

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 20M30
• 60H10
• 60H30

Additional information

Funding

This research is supported by the PhD program startup fund of Chong Qing Normal University (Grant No. 15XLB013) and the National Natural Science Fund advance research project of Chong Qing Normal University (Grant No. 16XYY22).