The Fractal Properties Of The Level Sets And Inverse Image Of N-dimension Non-degenerate Diffusion Processes

Let (F,P) be a complete probability space , and X(t}= be a N-dimension non- degenerate diffusion processes on it . The Holder continuity of N-dimension non-degenerate diffusion processes and Hausdorff dimension of graph sets and image sets have been settled by professor Yang in [1] . In this thesis , with the aid of this paper , the author has discussed the Hausdorff dimension and Packing dimension of the level sets and inverse image of N-dimension non-degenerate diffusion processes .Furthermore, the fractal properties of the level sets and inverse image of compact sets of N-dimension non-degenerate diffusion processes is also considered by professor Yang in [2] , and some new results are obtained in this paper .The main results are calculated as follows: 1. The Hausdorff dimension of level sets :2. The property of the level sets of compact sets:where T = [0,l], is a compact sets, and 3. The upper bound of Hausdorff dimension of level sets of compact sets:where T = [0,1], is a compact sets, 4. The Packing dimension of level sets :5. The Hausdorff dimension of inverse image:Where F is a compact sets.6. The Packing dimension of inverse image: Where F is a compact sets.