g-协方差和g-相关系数的几个性质  

Some Properties of g-Covariance and g-Correlation Coefficient

作　　者：郝涛[1] 

机构地区：[1]山东中医药大学理工学院,济南250355

出　　处：《应用概率统计》2012年第6期637-646,共10页Chinese Journal of Applied Probability and Statistics

摘　　要：介绍一类建立在g-期望基础之上新的非线性协方差—g-协方差.研究了g-协方差的几个性质,包括交换性、齐次性、可加性.在此基础上还得到当g-协方差同时满足齐次性和可加性的充要条件,即g关于z是线性的.发现基于g-期望的相关系数的值不介于±1之间,且它也不再反映两个随机变量间的线性关系.A new nonlinear covariance based on g-expectation, g-covariance, is introduced and some properties of g-covariance including commutativity, homogeneity, additivity are studied. According to these results, the sufficient and necessary condition of g-covariance satisfied homogeneity and additivity is obtained. That is g, a linear function of z. Correlation coefficient based on g-expectation does not rang from -1 to 1 and it does not reflect the linear relationship between two random variables, either.

关 键 词：倒向随机微分方程 G-期望 g-协方差 g-方差 g-相关系数 

分 类 号：O211.63[理学—概率论与数理统计] O211.6[理学—数学]