Some inequalities and limit theorems under sublinear expectations

Abstract

In this note, we study inequality and limit theory under sublinear expectations. We mainly prove Doob's inequality for submartingale and Kolmogrov's inequality. By Kolmogrov's inequality, we obtain a special version of Kolmogrov's law of large numbers. Finally, we present a strong law of large numbers for independent and identically distributed random variables under one-order type moment condition.

15 pages

References in corpus (6)

• A New Central Limit Theorem under Sublinear Expectations
• Strong laws of large numbers for sub-linear expectations
• Nonlinear Expectations and Stochastic Calculus under Uncertainty
• Law of Large Numbers and Central Limit Theorem under Nonlinear Expectations
• Sublinear Expectations and Martingales in discrete time
• General laws of large numbers under sublinear expectations

Cited by in corpus (1)

• Multi-dimensional central limit theorems and laws of large numbers under sublinear expectations