A law of the iterated logarithm sublinear expectations

Abstract

In this paper, motivated by the notion of independent identically distributed (IID) random variables under sub-linear expectations initiated by Peng, we investigate a law of the iterated logarithm for capacities. It turns out that our theorem is a natural extension of the Kolmogorov and the Hartman-Wintner laws of the iterated logarithm.

References in corpus (3)

• A New Central Limit Theorem under Sublinear Expectations
• Function spaces and capacity related to a Sublinear Expectation: application to G-Brownian Motion Pathes
• Moment bounds for IID sequences under sublinear expectations

Cited by in corpus (8)

• Donsker's invariance principle under the sub-linear expectation with an application to Chung's law of the iterated logarithm
• The convergence of the sums of independent random variables under the sub-linear expectations
• On the laws of the iterated logarithm under the sub-linear expectations without the assumption on the continuity of capacities
• Strong limit theorems for extended independent and extended negatively dependent random variables under non-linear expectations
• Self-normalized moderate deviation and laws of the iterated logarithm under G-expectation
• An Invariance Principle of G-Brownian Motion for the Law of the Iterated Logarithm under G-expectation
• On the law of the iterated logarithm under the sub-linear expectations
• A comparison theorem under sublinear expectations and related limit theorems