Donsker's invariance principle under the sub-linear expectation with an application to Chung's law of the iterated logarithm

Abstract

We prove a new Donsker's invariance principle for independent and identically distributed random variables under the sub-linear expectation. As applications, the small deviations and Chung's law of the iterated logarithm are obtained.

29 pages

References in corpus (4)

• A theoretical framework for the pricing of contingent claims in the presence of model uncertainty
• Rosenthal's inequalities for independent and negatively dependent random variables under sub-linear expectations with applications
• A New Central Limit Theorem under Sublinear Expectations
• Tightness, weak compactness of nonlinear expectations and application to CLT

Cited by in corpus (14)

• Rosenthal's inequalities for independent and negatively dependent random variables under sub-linear expectations with applications
• Exponential inequalities under sub-linear expectations with applications to laws of the iterated logarithm
• The convergence of the sums of independent random variables under the sub-linear expectations
• Strong limit theorems for extended independent and extended negatively dependent random variables under non-linear expectations
• Stochastic Calculus with respect to G-Brownian Motion Viewed through Rough Paths
• Lindeberg's central limit theorems for martingale like sequences under sub-linear expectations
• Self-normalized moderate deviation and laws of the iterated logarithm under G-expectation
• Convergence for sums of i. i. d. random variables under sublinear expectations
• Optimal Unbiased Estimation for Maximal Distribution
• Convergence to a self-normalized G-Brownian motion
• Equivalent conditions of complete convergence for weighted sums of sequences of i. i. d. random variables under sublinear expectations
• Convergences of Random Variables under Sublinear Expectations
• Equivalent conditions of complete $p$-th moment convergence for weighted sums of i. i. d. random variables under sublinear expectations
• Almost Sure Central Limit Theorem in Sub-linear Expectation Spaces