Sierpinski gasket上Brown运动与Hlder连续函数的关系

Relation between Brownian Motion on the Sierpinski Gasket and Hlder Continuous Functions

本文研究了Ｓｉｅｒｐｉｎｓｋｉｇａｓｋｅｔ上Ｂｒｏｗｎ运动｛Ｘ（ｔ），ｔ≥０｝与Ｈｏｌｄｅｒ连续函数的关系，得到了Ｘ（ｔ）的不动点集及水平集的Ｈａｕｓｄｏｒｆ维数，并说明了Ｘ（ｔ）没有极函数。

In this paper, we study the relation between Brownian motion{X(t),t≥0} on the Sierpinski gasket and Hlder continuous functions, obtain Hausdorff dimension of the fixed point set and level set of X(t) and explain why X(t) does not possess polar functions.