多维奥伦斯坦－乌伦贝克过程的一些统计性质

Some Statistical Properties of Multidimensional Ornstein-Uhlenbeck Processes

记为ｎ维奥伦斯坦－乌伦贝克过程，Ｘ＿ｊ（ｔ）由广义维纳积分，ｎ来确定，其｛Ｂ＿ｊ（ｔ），ｔ∈Ｒ￣１｝是相互独立且规范化的广义布朗运动过程。本文探讨了ｎ维奥伦斯坦－乌伦贝克过程｛Ｘ（ｔ），ｔ∈Ｒ￣１）和随机泛涵向量ｆ（Ｘ（ｔ））的一些统计特性，这里ｆ，ｆ＿１，…，ｆ＿ｎ都是ｎ元有界Ｂｏｒｅｌ可测函数。在此基础上再探讨随机泛函向量ｆ（Ｘ（ｔ））的预测向量，并给出一些关于预测向量以及格应的均方误差向量的解析表达式。

Ltx,be the n-dimensional Ornstein-Uhlenbeck processes,which are given by the following generallzed Wiener integralswhere{B_j(t),t∈ R￣1},j=1,2,…,n,are mutually independent,normalized generalized Brownian motion processes. In this paper,the author deals with some statistical propertiesof the n-dimensional Omstein-Uhlenbeck processes {X(t),t∈R￣1}and the stochastic functional vector f(X(t))=(f_1(X(t)),…,f_n(X(t)))￣T,t∈R￣1,where f,f_j,j=1,2,…,n,are bounded Borel measurable functions of n-varlables. And then the author discusses the non-linear predictor vector for the stochastic functional vector f(X(t))and presents some analytical formulas of the non-linear predictor vector and corresponding mean-square error vector.