非退化扩散过程样本轨道的Fractal性质

Fractal Properties of Sample Path of a Nondegenerate Diffusion Process

讨论了N维非退化扩散过程样本轨道的性质 ,并由此得到一维非退化扩散过程样本轨道的象集和逆象集的Hausdorff维数 .此外 ,研究了当N >4时 ,其样本轨道的二重点问题 .

Considered the properties of sample paths of a N-dimensional nondegenerate diffusion process, and obtained the Hausdorff dimensions of its image set and inverse image set for N = 1. Futhermore, for N > 4, its double points problem is also investigated.