Strassen's law of the iterated logarithm under sub-linear expectations

2022/12/21 by Wang-yun Gu, Zhang Li, Gu, Wang-yun +1
Decision Sciences · Mathematics · #60F15 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Probability and Risk Models #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2212.11103

openalex publication_date 2022/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish the Strassen's law of the iterated logarithm for independent and identically distributed random variables with 𝔼[X₁]=E[X₁]=0 and C_\mathbbV[X₁²]<∞ under sub-linear expectation space with a countably sub-additive capacity \mathbbV. We also show the LIL for upper capacity with σ=σ under some certain conditions.

Related

• A note on the cluster set of the law of the iterated logarithm under sub-linear expectations
• On the law of the iterated logarithm under the sub-linear expectations
• On the Law of the Iterated Logarithm for m-dependent stationary random variables under sub-linear expectations
• The moments of the maximum of normalized partial sums related to laws of the iterated logarithm under the sub-linear expectation
• Strong limit theorems for extended independent and extended negatively dependent random variables under non-linear expectations