典型随机动力系统的联合与边缘、条件概率密度的形态分析  

Shapes of Joint,Marginal,and Conditional Probability Densities of Typical Stochastic Dynamical Systems

作　　者：谢文贤[1] 唐亚宁[1] 蔡力[1] 林伟[1] XIE Wenxian;TANG Yaning;CAI Li;LIN Wei(Department of Applied Mathematics,Northwestern Polytechnical University,Xi'an 710129,China)

机构地区：[1]西北工业大学理学院应用数学系,陕西西安710129

出　　处：《高等数学研究》2019年第1期94-97,共4页Studies in College Mathematics

基　　金：中央高校基本科研业务费项目(3102017zy041);研究生高水平全英文课程(Mathematical Statistics)建设项目

摘　　要：本文刻画几类典型随机动力系统的二维稳态联合概率密度的形态,并通过引入"横"与"侧"认识角度观察联合概率密度这座"山峰",直观展现其与边缘、条件概率密度三者之间的联系并形成对随机变量独立性的立体认知.从而帮助学生增强对联合概率密度概念的直观认识,加深对三者概率密度相互联系的理解,也有助于相关教师对概率论教学与科研活动互动的促进.In this paper,the multifarious shapes of steady joint probability densities for several typical stochastic dynamical systems are displayed. From the different horizontal or vertical aspects of observation,the visualized descriptions of joint,marginal and conditional probability densities can be formed in virtue of assimilating joint probability density to a mountain . In that case,the viewpoint of an ancient poetry written by Su-Shi,a distinguished writer and poet,is introduced to illustrate the relationship of these three kinds of probability densities. Consequently,the independence of two or more random variables is also explicitly represented. The aforementioned is helpful for enriching the concept of joint probability density and enhancing the interaction of teaching and research related with probability theory.

关 键 词：二维连续型随机变量 二维联合概率密度 条件概率密度 边缘概率密度 非线性随机动力系统 

分 类 号：O211[理学—概率论与数理统计]