股票收益率的信息几何  

Information Geometry of Stock Return Process

作　　者：曹丽梅[1] 孙华飞[1] 张真宁[1] 

机构地区：[1]北京理工大学理学院,北京100081

出　　处：《北京理工大学学报》2007年第1期91-94,共4页Transactions of Beijing Institute of Technology

基　　金：国家自然科学基金资助项目(20331010)

摘　　要：基于信息几何建立股票收益率满足的概率分布族所构成的微分流形,给出流形的几何结构.算出流形的Fisher信息矩阵及其α-联络系数,获得流形在α-联络下的高斯曲率.由流形的α-测地线方程,求出α=0时的解.得到流形的α-散度,-αKullback散度及J-散度,并说明两种散度之间的关系以及各种特殊情况下的散度.Abstract： Constructs the differential manifold of stock return process based on information geometry, and gives its geometric structure such as the Fisher metric matrix and α-connection coefficients. The Gauss curvature and α-geodesic of the manifold are obtained in the sense of corresponding α- connection. Solution of the geodesic equation when α = 0 is thereby given. Also the α-divergence, α- Kullback divergence and J-divergence of the manifold are given, whilst the relation between the α- divergence and α-Kullback divergence are shown and the divergences in some special cases are given too.

关 键 词：股票收益率 散度 信息几何 α-联络 

分 类 号：O129[理学—数学]