几类与布朗运动有关的高斯过程的再生核Hilbert空间  

Reproducing Kernel Hilbert space of some Gaussian processes related to the Brownian motion

作　　者：艾晓辉[1] 孙阳 AI Xiaohui;SUN Yang(College of Science,Northeast Forestry University,Harbin 150040,China;College of Science,Harbin University of Science and Technology,Harbin 150080,China)

机构地区：[1]东北林业大学理学院,哈尔滨150040 [2]哈尔滨理工大学理学院,哈尔滨150080

出　　处：《黑龙江大学自然科学学报》2022年第2期160-164,共5页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(31570492)。

摘　　要：研究了带线性漂移的布朗运动、Demeaned布朗运动以及Demeaned布朗桥的再生核Hilbert空间。首先,对于带线性漂移的布朗运动,利用其协方差函数进行了Karhunen-Loève(KL)展开,并用特征函数作为基函数构造出了再生核Hilbert空间。其次,对于Demeaned布朗运动,给出了其协方差函数,定义了相应的内积,构造出了再生核Hilbert空间。最后,对于Demeaned布朗桥,给出了其协方差函数,定义了相应的内积,构造出了再生核Hilbert空间。The Brownian Motion with linear drift, demeaned Brownian motion and reproducing kernel Hilbert spaces with demeaned Brownian Bridge are investigated. Firstly, for Brownian motion with linear drift, the covariance function is utilized for Karhunen-Loève(KL) expansion, and the eigenfunctions, as the base functions, are used to construct the reproducing kernel Hilbert space(RKHS). Secondly, for demeaned Brownian motion, the covariance function is given, the relevant inner product is defined, and the RKHS is constructed. At last, the covariance function and relevant inner product are provided to find RKHS with the demeaned Brownian Bridge.

关 键 词：带线性漂移的布朗运动 Demeaned布朗运动 Demeaned布朗桥 再生核HILBERT空间 

分 类 号：O211.1[理学—概率论与数理统计]