Equidistribution and Brownian motion on the Sierpiński gasket

Peter J. Grabner; Robert F. Tichy

doi:10.1007/BF01332824

Equidistribution and Brownian motion on the Sierpiński gasket

Peter J. Grabner^*, Robert F. Tichy

^*Corresponding author for this work

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

Abstract

We introduce several concepts of discrepancy for sequences on the Sierpiński gasket. Furthermore a law of iterated logarithm for the discrepancy of trajectories of Brownian motion is proved. The main tools for this result are regularity properties of the heat kernel on the Sierpiński gasket. Some of the results can be generalized to arbitrary nested fractals in the sense of T. Lindstrøm.

Original language	English
Pages (from-to)	147-164
Number of pages	18
Journal	Monatshefte fur Mathematik
Volume	125
Issue number	2
DOIs	https://doi.org/10.1007/BF01332824
Publication status	Published - 1 Jan 1998

Keywords

Diffusion processes
Discrepancy
Fractals
Uniform distribution

ASJC Scopus subject areas

General Mathematics

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10.1007/BF01332824

Cite this

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abstract = "We introduce several concepts of discrepancy for sequences on the Sierpi{\'n}ski gasket. Furthermore a law of iterated logarithm for the discrepancy of trajectories of Brownian motion is proved. The main tools for this result are regularity properties of the heat kernel on the Sierpi{\'n}ski gasket. Some of the results can be generalized to arbitrary nested fractals in the sense of T. Lindstr{\o}m.",

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AB - We introduce several concepts of discrepancy for sequences on the Sierpiński gasket. Furthermore a law of iterated logarithm for the discrepancy of trajectories of Brownian motion is proved. The main tools for this result are regularity properties of the heat kernel on the Sierpiński gasket. Some of the results can be generalized to arbitrary nested fractals in the sense of T. Lindstrøm.

KW - Diffusion processes

KW - Discrepancy

KW - Fractals

KW - Uniform distribution

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Equidistribution and Brownian motion on the Sierpiński gasket

Abstract

Keywords

ASJC Scopus subject areas

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