实正态过程线性组合之均方不定积分的正态性的证明  

Proof of Normality of Mean Square Indefinite Integral of Linear Combination of Real Normal Processes

作　　者：吕芳[1] LYU Fang(School of Mathematical Sciences,Luoyang Normal University,Luoyang,Henan 471934,China)

机构地区：[1]洛阳师范学院数学科学学院,河南洛阳471934

出　　处：《平顶山学院学报》2022年第5期1-4,共4页Journal of Pingdingshan University

基　　金：国家自然科学基金(61902166)。

摘　　要：介绍了均方不定积分的概念,将m个均方连续且相互独立的实正态过程做线性运算,得到一个线性组合,证明了这个线性组合的均方不定积分仍为实正态过程,并给出了此实正态过程的任意有限维特征函数的具体表达式.This paper introduces the concept of mean square indefinite integral.These m real normal processes with mean square continuous and independent are linearized and a linear combination is obtained.It is proved that the mean square indefinite integral of the linear combination is still a real normal process.The concrete expression of the arbitrary finite dimensional eigenfunction of the real normal process is given.

关 键 词：实正态过程 线性组合 均方不定积分 有限维特征函数 

分 类 号：O211.62[理学—概率论与数理统计]