An exponential inequality for widely orthant dependent random variables and its application to a first-order autoregressive model

This study develops an exponential inequality for widely orthant dependent random variables. We establish complete convergence and derive a convergence rate of O(1)(log2n)α1+αn−α1+α for the strong law of large numbers, where 0<α≤1. As an application to a linear model, we obtain the strong law of large numbers with a convergence rate of O(1)(log2n)2α1+αn−2α1+α, where 0<α<1. Numerical simulations are provided to illustrate and support the theoretical results.