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 prov...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.展开更多
A large Type Ⅳμ solar radio burst was observed at Yunnan observatory on December 16, 1988. The burst was associated by a coronal mass ejection (CME) with the radio signature of Type Ⅱ and Type Ⅳ bursts. On the bas...A large Type Ⅳμ solar radio burst was observed at Yunnan observatory on December 16, 1988. The burst was associated by a coronal mass ejection (CME) with the radio signature of Type Ⅱ and Type Ⅳ bursts. On the basis of Beijing Huairou magnetogram of AR5278, power law distribution of electrons of the source region is calculated. It is suggested that the Type Ⅳμ burst associated with CME was due to the gyrosynchrotron radiation of high energy electrons trapped by magnetic field. Finally, some quantitative and qualitative explanations are proposed.展开更多
基金Supported by the National Natural Science Foundation of China (No.10071072)the project supported by Natural Science Fundation of Zhejiang Province (No.101016).
文摘In this paper, we obtain the invariance principle for linear processes generated by a negatively associated sequence.
文摘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.
文摘A large Type Ⅳμ solar radio burst was observed at Yunnan observatory on December 16, 1988. The burst was associated by a coronal mass ejection (CME) with the radio signature of Type Ⅱ and Type Ⅳ bursts. On the basis of Beijing Huairou magnetogram of AR5278, power law distribution of electrons of the source region is calculated. It is suggested that the Type Ⅳμ burst associated with CME was due to the gyrosynchrotron radiation of high energy electrons trapped by magnetic field. Finally, some quantitative and qualitative explanations are proposed.
