Precise Asymptotics Of The Complete Convergence For Lai Law Under Sublinear Expectations

Precise asymptotics is a branch of limit theory.In recent years,the study of the precise asymptotics of random variable sequence in the law of the iterated logarithm and complete convergence has been developed to a certain extent.However,the assumptions of classical limit theory are more idealistic,and the research is mostly carried out under the clear conditions determined by the model,which is quite di?erent from the reality of life.With the increasing demand for the accuracy and robustness of risk measurement,experts and scholars have proposed nonlinear expectation theory in research to solve the problem of uncertainty in probability and distribution,among which the most representative sublinear expectations have gradually become a research hotspot.Due to the capacity and sublinear expectations having their own sub-additivity,many commonly used research methods are no longer e?ective,which increases the di culty of research.Therefore,the traditional concepts in probability space as well as the generalization of classical theories under sublinear expectation space are of great research value.Furthermore,the framework of sublinear expectation theory has been gradually improved and applied to many fields such as statistics,finance,economics,etc.This paper mainly studies the precise asymptotics of the complete convergence for Lai law under sublinear expectations.The article handled the problem by using the closed form of the one-sided tail capacity of G-normal distribution,and finally obtained the corresponding results.Finally,this paper also studied the extendability of the existence of the mean after the truncation of random variables.The conclusion of this paper generalizes the results of Sp?ataru and its form enriches the limit theories under sublinear expectations,which may have potential applications in financial markets.The first chapter mainly introduces the research background of precision asymptotics and complete convergence,the current status of research at home and abroad,Lai law,the main work of Sp?ataru and the research content of this paper.The second chapter introduces some concepts as well as necessary lemmas related to sublinear expectation theory and limit theory to support subsequent proofs.The third chapter discusses the precise asymptotics for Lai’s complete convergence theorem under sublinear expectations and conducts an extended study for the condition that the mean of the random variables is not zero after making truncation.