The Nature Of Ergodicity And The Correlation Function Of Self-similar Process

In practical applications,Mean function and correlation function of Random process is very important.However,The characteristics of these figures difficult to obtain,Oftenly for a random process X(t),We can only be obtained a sample function X(t) through test,Or the corresponding value X(t₀),X(t₁),...,X(t_n) of a samples function in a number of times t₀,t₁,...,t_n,Requiring ergodic of random process to estimate the problem of the number features.This paper introduces ergodicity of the self-similar process,The first chapter is the introduction,Introduced the background of ergodicity theorem;The second chapter is knowledge to prepare,Introduced the basic status of ergodic theorem and related definitions;ChapterⅢis the main theorem, Respectively,Its some properties of correlation function are given in detail,And when {X(t),t≥0} is the self-similarity process of mean-square continuous,And ergodicity of its mean function,correlation function and the distribution function.