Moderate Deviation Principle for Linear Processes Generated by Dependent Sequences under Sub-Linear Expectation

Abstract

We are interested in the linear processes generated by dependent sequences under sub-linear expectation. Using the Beveridge–Nelson decomposition of linear processes and the inequalities, the moderate deviation principle for linear processes produced by an m-dependent sequence is established. We also prove the upper bound of the moderate deviation principle for linear processes produced by negatively dependent sequences via different methods from m-dependent sequences. These conclusions promote and improve the corresponding results from the traditional probability space to the sub-linear expectation space.

Keywords

• moderate deviation principle
• linear process
• m-dependent
• negatively dependent
• sub-linear expectation