Large deviation principle for linear processes generated by real stationary sequences under the sub-linear expectation

Abstract

Let $\left\{X_k={\sum }_{j=-\infty }^{+\infty }{a}_j{\xi }_{k-j}, k\ge 1\right\}$ be the linear processes, where $\{a_j, j\in \mathbb{Z}\}$ is an absolutely summable sequence of real numbers and ${\sum }_{j=-\infty }^{+\infty }{a}_j\ne 0,$ $\{{\xi }_j,j\in \mathbb{Z}\}$ is a sequence of real stationary independent random variables under the sub-linear expectation space $(\Omega ,\mathcal{H},\mathbb{E}).$ In the framework of sub-linear expectation space, the Beveridge–Nelson decomposition of linear processes and the sub-additivity of capacity are used to establish the large deviation principle for linear processes in the sense of upper probability.

Keywords:

• Large deviation principle
• sub-linear expectation
• linear process
• stationary sequences

MATHEMATICS SUBJECT CLASSIFICATION:

• 60F10

Additional information

Funding

The paper was supported by National Natural Science Foundation of China (Grant No. 11771178, 12171198); the Science and Technology Development Program of Jilin Province (Grant No. 20210101467JC) and Science and Technology Program of Jilin Educational Department during the “13th Five-Year” Plan Period (Grant No. JJKH20200951KJ) and Fundamental Research Funds for the Central Universities.