TRANSITION DENSITIES FOR BROWNIAN-MOTION ON THE SIERPINSKI CARPET

被引:117
作者
BARLOW, MT [1 ]
BASS, RF [1 ]
机构
[1] UNIV WASHINGTON,DEPT MATH,SEATTLE,WA 98195
关键词
D O I
10.1007/BF01192060
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
Upper and lower bounds are obtained for the transition densities p(t, x, y) of Brownian motion on the Sierpinski carpet. These are of the same form as those which hold for the Sierpinski gasket. In addition, the joint continuity of p(t, x, y) is proved, the existence of the spectral dimension is established, and the Einstein relation, connecting the spectral dimension, the Hausdorff dimension and the resistance exponent, is shown to hold.
引用
收藏
页码:307 / 330
页数:24
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