Large Powers asymptotics, Khinchin families and Lagrangian distributions

2022/01/27 by Víctor J. Maciá, Fernández, José L., Maciá, Víctor J. · 1 citation
Economics, Econometrics and Finance · Mathematics · #05A16 #30B10 #60F05 #60F99 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Probability and Statistical Research

paper · pdf · doi:10.48550/arxiv.2201.11746

openalex publication_date 2022/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper delves on the versatility of the theory of Khinchin families for asymptotic estimation. We show that in combination with Local Central Limit theorems for lattice variables, Khinchin families furnish a convenient and unified framework to deal with asymptotic results of the coefficients of large powers of power series. We revisit in the present paper this classical theme from that point of view, obtaining clean new proofs and a number of new results. Asymptotic results for the coefficients of solutions of Lagrange's equation fall naturally into this combined framework. We provide a direct proof of an extension of the Otter and Meir-Moon asymptotic formula as well as asymptotic results for families of Lagrangian probability distributions.

Cited by

• Galton-Watson processes, simple varieties of trees and Khinchin families

Related

• The Theory of Khinchin Families
• Asymptotic results for families of power series distributions
• Law of Large Numbers and Central Limit Theorems by Jack Generating Functions
• Une étude asymptotique probabiliste des coefficients d'une série entière
• Growth of power series with nonnegative coefficients, and moments of power series distributions