Weak and strong laws of large numbers for sub-linear expectation

Abstract

In this paper, we derive a new form of weak laws of large numbers for sub-linear expectation and establish the equivalence relation among this new form and the other two forms of weak laws of large numbers for sub-linear expectation. Moreover, we obtain the strong laws of large numbers for sub-linear expectation under a general moment condition by applying our new weak laws of large numbers.

Keywords:

• Weak laws of large numbers
• strong laws of large numbers
• sub-linear expectation
• capacity

MATHEMATICS SUBJECT CLASSIFICATION (2010):

• 60F15

Acknowledgements

The author would like to thank Professor Zengjing Chen for his help. He also thank the editor and anonymous referees for their valuable comments and useful suggestions.