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 clockw...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.展开更多
文摘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.
