Strong law of large numbers for linear processes under sublinear expectation

Abstract

In the framework of sublinear expectation, we investigate the limit behavior of linear processes and derive a strong law of large numbers for them. It turns out that our theorem is a natural extension of the one in the classical linear case, and we can derive the corresponding strong law of large numbers for independent random variables under sublinear expectation from our result.

Keywords:

• Strong law of large numbers
• linear processes
• sublinear expectation

Acknowledgments

The author would like to thank the editors and anonymous reviewers for their valuable comments and suggestions.

Disclosure statement

There are no relevant financial or non-financial competing interests to report.

Additional information

Funding

This work is supported by National Natural Science Foundation of China (Grant No. 12101367), Shandong Provincial Natural Science Foundation, China (Grant No. ZR2021QA066).