Strong law of large numbers for $m$-dependent and stationary random variables under sub-linear expectations

Abstract

The arm of this paper is to establish the strong law of large numbers (SLLN) of $m$-dependent random variables under the framework of sub-linear expectations. We establish the SLLN for a sequence of independent, but not necessarily identically distributed random variables. The study further extends the SLLN to $m$-dependent and stationary sequence of random variables with the condition $C_{\mathbb V}(|X_1|)<\infty$ which is the sufficient and necessary condition of SLLN in the case of independent and identically distributed random variables.