Estimates of transition densities for Brownian motion on nested fractals

Takashi Kumagai

doi:10.1007/BF01192133

Estimates of transition densities for Brownian motion on nested fractals

Takashi Kumagai^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

77 Citations (Scopus)

Abstract

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, Hölder order of the resolvent densities, sample paths and local times are obtained. The results are obtained using the theory of multi-type branching processes.

Original language	English
Pages (from-to)	205-224
Number of pages	20
Journal	Probability Theory and Related Fields
Volume	96
Issue number	2
DOIs	https://doi.org/10.1007/BF01192133
Publication status	Published - 1993 Jun
Externally published	Yes

Keywords

Mathematics Subject Classification: 60J60, 60J65, 60J80

ASJC Scopus subject areas

Analysis
Statistics and Probability
Statistics, Probability and Uncertainty

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10.1007/BF01192133

Cite this

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AB - 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, dJ, related to the "shortest path metric" and "chemical exponent" on nested fractals. Further, Hölder order of the resolvent densities, sample paths and local times are obtained. The results are obtained using the theory of multi-type branching processes.

KW - Mathematics Subject Classification: 60J60, 60J65, 60J80

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Estimates of transition densities for Brownian motion on nested fractals

Abstract

Keywords

ASJC Scopus subject areas

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