Functional Erdös-Rényi law of large numbers for nonconventional sums under weak dependence

2016/08/05 by Yuri Kifer, Kifer, Yuri
Decision Sciences · Economics, Econometrics and Finance · #37D20 #37D35 #60F10 #60F15 #60F17 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1608.01851

openalex publication_date 2016/08/05 · openalex created_date 2016/08/23 · openalex updated_date 2026/07/28

Abstract

We obtain a functional Erd\H os-R' enyi law of large numbers for "nonconventional" sums of the form \Sig_n=∑_m=1ⁿF(X_m,X_2m,...,X_{ℓ m}) where X₁,X₂,... is a sequence of exponentially fast ψ-mixing random vectors and F is a Borel vector function extendin in several directions our previous result concerning i.i.d. random variables X₁,X₂,....

Related

• Erdös-Rényi law of large numbers in the averaging setup
• Marcinkiewicz-Zygmund Strong Law of Large Numbers for Pairwise i.i.d. Random Variables
• A Generalization of the Petrov Strong Law of Large Numbers
• An Extension of Feller's Strong Law of Large Numbers
• On strong law of large numbers for non identically distributed random variables