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.

Keywords

Sub-linear expectation / Capacity / Central limit theorem / Invariance principle / Chung’s law of the iterated logarithm / Small deviation

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