设dX(t)=σ(X(t))dB(t)+β(X(t))dt为一非退化d(d≥3)维扩散过程.证明了:(i)3维非退化扩散过程没有4重时集和4重点集;(ii)4维非退化扩散过程没有3重时集和3重点集;(iii)5维以上的非退化扩散过程没有2重时集和2重点集。
Let dX(t)=σ(X(t))dB(t)+β(X(t))dt be a d-dimensional nondegenerate diffusion processes. It is proved that (i) if d = 3, then there are no 4 triple time set and 4 triple points set for X ( t ), a. s. (ii) if d = 4, then there are no 3 triple time set and 3 triple points set for X ( t ), a. s. (iii) ff d ≥5, then there are no 2 triple time set and 2 triple points set for X(t),a.s.