广义Wiener过程及其性质

Wiener Process in the Naive Sense and its Properties

本文在文[1]的基础上引入中心椭球等高过程的概念,进而给出了广义Wiener过程{x(t),t≥0}的定义,并证明了它的两个性质:(1)数字特征:EX(t)=0,DX(t)=σ~2t,Γ(s,t)=σ~2min{s,t};(2(正交分解式X(t)=sum from n=0 to ∞ ((((1/2)(2a))σ)/π(n+1/2))sin[π/a(n+1/2)t]§_n,t∈[0,a]其中{§_n)是标准正交的二阶矩变量序列。

In this paper, based on paper [1] , We introduce the notion of the process of the central ellipsoidal equal height, and further give the definition of Wiener process {X(t), t≥0 } in the naive sense, and we have proved its two properties: (1) characteristic numbres: EX(t)=0, DX(t) = σ2t, Γ(s1, t)=σ2min{s,t}; ( 2 orthogonal decomposition.where {ξa} is the sequence of the orthonormal second order variable.