Almost sure convergence theorems for arrays under sub-linear expectations

Abstract

In this work, inspired by the extended negatively dependent arrays, we want to obtain a limit theorem on almost sure convergence relying on non-additive probabilities. Meanwhile, we offer two appropriate upper integration conditions as an application, allowing us to derive deterministic bounds based on logarithm. Furthermore, these results extend the limit theorems in classical probability space.

Keywords

• sub-linear expectation
• almost sure convergence
• extended negative dependence
• law of the logarithm
• weakly mean dominated