Complete moment convergence for the widely orthant dependent linear processes with random coefficients

Abstract

The main purpose of this paper is to obtain the complete moment convergence for widely orthant dependent linear processes with random coefficients in form $X_t={\sum }_{j=-\infty }^{\infty }{A}_j{\epsilon }_{t-j},$ where $\{{\epsilon }_n,n\in \mathbb{Z}\}$ is a sequence of stochastically dominated WOD random variables and $\{A_n,n\in \mathbb{Z}\}$ is a sequence of random variables.

KEYWORDS:

• Complete moment convergence
• widely orthant dependent random variables
• linear processes
• random coefficients

2019 MSC:

• 60F15
• 60G07

Additional information

Funding

The research of the first author was supported by the National Natural Science Foundation of China (Grant No. 11571058), the Fundamental Research Funds for the Central Universities (Grant No. DUT18LK18), the Dalian High Level Talent Innovation Program (Grant No. 2015R051) and the Hihe-level innovative and entrepreneurial talents support plan in Dalian (Grant No. 2017RQ041).