DIFFUSION PROCESSES ON PRINCIPAL BUNDLES AND DIFFERENTIAL OPERATORS ON THE ASSOCIATED BUNDLES  

作　　者：王正栋 郭懋正 钱敏 

机构地区：[1]Department of Mathematics, Peking University, Beijing 100871, PRC

出　　处：《Science China Mathematics》1992年第4期385-398,共14页中国科学：数学（英文版）

基　　金：Project supported by TWAS GR no. 86-30.

摘　　要：The lifting of diffusion processes and differential operators on a Riemannian base spaceM to diffusion processes on a principal bundle P and differential operators on the associatedbundle are studied. It has been proved that the infinitesimal generator of the lifted processcan be seen as a second-order differential operator on the section space Γ of the associatedbundle, which is just the lifted operator of the infinitesimal generator of the diffusion pro-cess on the base space. The covariant Feynman-Kac formula on a non-trival principal bundlehas been given. which generalizes the formula given by S. Albeverio. Furthermore, as anapplication, a geometric proof of the Girsanov-Cameron-Martin theorem (GCM theorem) onthe Riemannian manifolds has been given.The lifting of diffusion processes and differential operators on a Riemannian base spaceM to diffusion processes on a principal bundle P and differential operators on the associatedbundle are studied. It has been proved that the infinitesimal generator of the lifted processcan be seen as a second-order differential operator on the section space Γ of the associatedbundle, which is just the lifted operator of the infinitesimal generator of the diffusion pro-cess on the base space. The covariant Feynman-Kac formula on a non-trival principal bundlehas been given. which generalizes the formula given by S. Albeverio. Furthermore, as anapplication, a geometric proof of the Girsanov-Cameron-Martin theorem (GCM theorem) onthe Riemannian manifolds has been given.

关 键 词：diffusion process INFINITESIMAL GENERATOR CONNECTION ASSOCIATED bundle. 

分 类 号：N[自然科学总论]