关于实正态过程广义均方积分的正态性的一种证明

打开文本图片集

中图分类号：0211.62 文献标识码：A 文章编号：1674-0033(2025)06-0022-04

A Proof of Normality of Generalized Mean Square Integral of Normal Process

LU Fang

(Department of Mathematics,LuoyangNormal University,Luoyang471934,Henan)

Abstract: The proof method for the normality of the generalized mean square integral of real normal processes is studied.Starting from the conclusion that the mean square integral of areal normal process over a finite interval is stilla normal process,byusing the properties of multi-dimensional normal random vectors and mean square limits,the generalized mean square integral process is proved to be a normal process by proving that the vector formed by any finite number of elements in the generalized mean square integral process is a multi-dimensional normal vector.This proof method starts from the definition of the normal process and uses relatively basic concepts and theories to draw conclusions.The proof process is more concise.While proving theconclusion,it also calculates the numerical characteristics of the generalized mean square integral process (including the mean function,correlation function and covariance function) and any finite-dimensional characteristic function.

Key words:real normal process; generalized mean-square integration; finite dimensional characteristic functions

在随机过程理论中，正态过程（又称高斯过程)是一类重要的二阶矩过程，可视为联合正态分布的无限维延伸。（剩余11265字）