摘要
The projection process along a simple closed smooth curve of a n onexplosive diffusion process on a complete Riemannian manifold is defined in p r obabilistic way. The winding numbers of the projection process are clockwi se and counterclockwise given. The symmetry of the diffusion process is shown to be equi valent to that for any closed smooth curve, the long time average winding numbe rs of the projection process in two different directions are equal.
The projection process along a simple closed smooth curve of a nonexplosive diffusion process on a cornplete Riemannian manifold is defined in probabilistic way. The winding numbers of the pmjection process are clockwise and counterclockwise given. The symmetry of the diffusion process is shown to be equivalent to that for any closed smooth curve. the long time average winding numbers of the projection process in two different directions are equal.
基金
ProjectsupportedbytheNationalNaturalScienceFoundationofChina (GrantNo .195 710 4 5 )andtheDoctoralProgramFoundationofInstitutionofHigherEducationand 86 3Program .
