Complete convergence theorems for moving average process generated by independent random variables under sub-linear expectations

Abstract

The research of convergence properties of moving average process is a challenging field of limit theorems. The aim of this article is to provide a method to prove the complete convergence and complete integral convergence of moving average process for independent random variables in sub-linear expectation space. The results obtained in the article are the extensions of some complete convergence theorems under classical probability space.

KEYWORDS:

• Moving average process
• complete integral convergence
• independent random variables
• sub-linear expectation

MSC2020 Subject Classifications:

• 60F15

Additional information

Funding

This paper was supported by the National Natural Science Foundation of China (12061028) and Guangxi Colleges and Universities Key Laboratory of Applied Statistics.