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

来源：

PROBABILITY THEORY AND RELATED FIELDS | 1992年 / 91卷 / 3-4期

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

页码：307 / 330

页数：24

共 20 条

[1]

BANDT C, 1990, SEFL SIMILAR SETS, V6

[2] LOCAL-TIMES FOR BROWNIAN-MOTION ON THE SIERPINSKI CARPET [J].

BARLOW, MT ;

BASS, RF .

PROBABILITY THEORY AND RELATED FIELDS, 1990, 85 (01) :91-104

[3] NECESSARY AND SUFFICIENT CONDITIONS FOR THE CONTINUITY OF LOCAL TIME OF LEVY PROCESSES [J].

BARLOW, MT .

ANNALS OF PROBABILITY, 1988, 16 (04) :1389-1427

[4]

BARLOW MT, 1989, ANN I H POINCARE-PR, V25, P225

[5] BROWNIAN-MOTION ON THE SIERPINSKI GASKET [J].

BARLOW, MT ;

PERKINS, EA .

PROBABILITY THEORY AND RELATED FIELDS, 1988, 79 (04) :543-623

[6] RESISTANCE AND SPECTRAL DIMENSION OF SIERPINSKI CARPETS [J].

BARLOW, MT ;

BASS, RF ;

SHERWOOD, JD .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1990, 23 (06) :L253-L258

[7] ON THE RESISTANCE OF THE SIERPINSKI CARPET [J].

BARLOW, MT ;

BASS, RF .

PROCEEDINGS OF THE ROYAL SOCIETY-MATHEMATICAL AND PHYSICAL SCIENCES, 1990, 431 (1882) :345-360

[8]

BASS RF, IN PRESS ANN PROBAB

[9]

FABES EB, 1986, ARCH RATION MECH AN, V96, P328

[10]

FUKUSHIMA M, IN PRESS J POTENTIAL

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