Strong law of large numbers and complete convergence for non-identically distributed WOD random variables

ABSTRACT

In this paper, we establish the strong law of large numbers and complete convergence for non-identically distributed WOD random variables. We derive some new inequalities of Fuk–Nagaev type for the sums of non-identically distributed WD random variables. All these results further extend and refine previous ones.

KEYWORDS:

• Strong law of large numbers
• complete convergence
• widely orthant dependent
• Fuk–Nagaev type inequalities

Acknowledgements

The authors would like to thank the anonymous referees for their valuable suggestion and helpful comments which greatly improved the earlier version of this article.

Additional information

Funding

This research was supported by Nature Science Foundation of Liaoning Province (No. 201602188), Research Foundation for Doctor of Dalian Minzu University (No. 110066), Doctor Support Fund of Liaoning Province (No. 201601088) and Nature Science Foundation of Inner Mongolia Autonomous Region (No. 2017MS(LH)0106).