Limit Theory Of Recording Time And Its Associated Counting Processes

The record values can well reflect the changing process of the sequence of random variables,and its research has been a hot topic in academic circles in recent decades.The record values have good research value in academic research and real life.In terms of academic research,for example: the limit theory of record times interval,the sequence of random variables obey standard exponential distribution,Beta distribution,and Gumbel distribution.The distribution of record values sequences and the central limit theorem of their partial sums.Random variable sequences obey the distributed Weiwei distribution,Burr distribution,and Frechét distribution of record values sequences and their partial sum central limit theorems.In real life,such as: the highest output value of rice in the past years,the highest water level value in the flood years,the highest increase of stocks in consecutive days,and the best scores of athletes in the competition.The above examples show that the record values have important research significance in academic research and real life.At present,no matter in China or abroad,the research on record values and record times is more and more extensive,and a series of research results have been achieved.This article mainly studies the limit theory of recording time and its related counting process.Firstly,it introduces the domestic and foreign research status of record times,record values,complete convergence and precise asymptoticity.The definition and nature of the related counting process;then,in order to study the limit theorem of record times and related counting process,we give some basic theorems as the basis of theoretical proof;Next,by giving the relationship between the weighting parameters ?and ?,we obtain the limit theorem after the count variable is increased in weight and then the limit theorem of the record times and its related counting process is studied.Finally,the summary and prospect of this paper are given.