ESTIMATES OF TRANSITION DENSITIES FOR BROWNIAN-MOTION ON NESTED FRACTALS

被引：99

作者：

KUMAGAI, T

机构：

[1] Department of Mathematics, Osaka University, Osaka, 560, Toyonaka

来源：

PROBABILITY THEORY AND RELATED FIELDS | 1993年 / 96卷 / 02期

关键词：

D O I：

10.1007/BF01192133

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：

We obtain upper and lower bounds for the transition densities of Brownian motion on nested fractals. Compared with the estimate on the Sierpinski gasket, the results require the introduction of a new exponent, d(J), related to the ''shortest path metric'' and ''chemical exponent'' on nested fractals. Further, Holder order of the resolvent densities, sample paths and local times are obtained. The results are obtained using the theory of multi-type branching processes.

引用

页码：205 / 224

页数：20

共 50 条

[11] TRANSITION-STATE AND BROWNIAN-MOTION THEORIES OF SOLITONS
SKINNER, JL
WOLYNES, PG
[J]. JOURNAL OF CHEMICAL PHYSICS, 1980, 73 (08): : 4015 - 4021
[12] REARRANGEMENTS OF BROWNIAN-MOTION
KAUFMAN, R
[J]. ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1974, 31 (01): : 71 - 73
[13] OSCILLATING BROWNIAN-MOTION
KEILSON, J
WELLNER, JA
[J]. JOURNAL OF APPLIED PROBABILITY, 1978, 15 (02) : 300 - 310
[14] FUNCTIONS OF BROWNIAN-MOTION
WALSH, JB
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 49 (01) : 227 - 231
[15] QUANTUM BROWNIAN-MOTION
OPPENHEIM, I
ROMEROROCHIN, V
[J]. PHYSICA A, 1987, 147 (1-2): : 184 - 202
[16] RELATIVISTIC BROWNIAN-MOTION
CAUBET, JP
[J]. ADVANCES IN APPLIED PROBABILITY, 1976, 8 (02) : 230 - 231
[17] ALL THAT BROWNIAN-MOTION
DURR, D
[J]. LECTURE NOTES IN PHYSICS, 1982, 173 : 119 - 135
[18] SQUARE OF BROWNIAN-MOTION
NOMOTO, H
[J]. NAGOYA MATHEMATICAL JOURNAL, 1975, 59 (DEC) : 1 - 8
[19] BROWNIAN-MOTION OF A MIRROR
MARSHALL, TW
[J]. PHYSICAL REVIEW D, 1981, 24 (06) : 1509 - 1515
[20] BROWNIAN-MOTION ON A HYPERSURFACE
VANDENBERG, M
LEWIS, JT
[J]. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1985, 17 (MAR) : 144 - 150

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