On nonlinear weak law of large numbers

2025/06/09 by Alina Akhmiarova, Akhmiarova, Alina, A. Yu. Veretennikov +1
Decision Sciences · Mathematics · Physics and Astronomy · #60F15 #FOS: Mathematics #Mathematical and Theoretical Analysis #Probability (math.PR) #Probability and Risk Models #Quantum Mechanics and Applications

paper · pdf · doi:10.48550/arxiv.2506.07470

openalex publication_date 2025/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A new version of a weak nonlinear law of large numbers proposed. The existence of the first moment for any summand is not assumed. The assumption of independence is understood in the nonlinear sense, and may be further a little relaxed.

Citations

• On the Law of Large Numbers for non-equally distributed weakly dependent random variables
• Stein's Method for Law of Large Numbers under Sublinear Expectations
• Limit theorems with rate of convergence under sublinear expectations
• Two laws of large numbers for sublinear expectations
• A strong law of large numbers for non-additive probabilities
• Nonlinear Expectations and Stochastic Calculus under Uncertainty

Related

• Strong law of large numbers with concave moments
• On the Law of Large Numbers for non-equally distributed weakly dependent random variables
• On a Proof of the Strong Law of Large Numbers
• On a General Approach to the Strong Laws of Large Numbers
• On strong law of large numbers for non identically distributed random variables