A law of the iterated logarithm under sublinear expectations

Zengjing Chen · Feng Hu

64 citations0/0 files storedJournal of Financial Engineering

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Stochastic processes and financial applications Probability and Risk Models Fuzzy Systems and Optimization

Abstract

In this paper, with the notion of independent and identically distributed (IID) random variables under sublinear expectations initiated by Peng, we develop a law of the iterated logarithm (LIL) for capacities. It turns out that our theorem is a natural extension of the Kolmogorov and the Hartman–Wintner LIL.

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References

2007G-Expectation, G-Brownian Motion and Related Stochastic Calculus of Itô Type 2010Function Spaces and Capacity Related to a Sublinear Expectation: Application to G-Brownian Motion Paths 2008Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation 2009Survey on normal distributions, central limit theorem, Brownian motion and the related stochastic calculus under sublinear expectations 2005NONLINEAR EXPECTATIONS AND NONLINEAR MARKOV CHAINS 2008A New Central Limit Theorem under Sublinear Expectations

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2022Strong Limit Theorems for Extended Independent Random Variables and Extended Negatively Dependent Random Variables under Sub-Linear Expectations 2014How big are the increments of G-Brownian motion?2020The Convergence of the Sums of Independent Random Variables Under the Sub-linear Expectations 2021On the laws of the iterated logarithm under sub-linear expectations

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