Large deviations for Brownian motion on the Sierpinski gasket

Gerard Ben Arous, Takashi Kumagai

Research output: Contribution to journalArticle

Abstract

We study large deviations for Brownian motion on the Sierpinski gasket in the short time limit. Because of the subtle oscillation of hitting times of the process, no large deviation principle can hold. In fact, our result shows that there is an infinity of different large deviation principles for different subsequences, with different (good) rate functions. Thus, instead of taking the time scaling ε→0, we prove that the large deviations hold for εn z≡(25)nz as n→∞ using one parameter family of rate functions Iz(z∈[25,1)). As a corollary, we obtain Strassen-type laws of the iterated logarithm.

Original languageEnglish (US)
Pages (from-to)225-235
Number of pages11
JournalStochastic Processes and their Applications
Volume85
Issue number2
StatePublished - Feb 1 2000

Fingerprint

Sierpinski Gasket
Large Deviation Principle
Rate Function
Brownian movement
Large Deviations
Brownian motion
Hitting Time
Law of the Iterated Logarithm
Subsequence
Corollary
Infinity
Scaling
Oscillation
Large deviations
Family

Keywords

  • 60F10
  • 60J60
  • 60J80
  • Branching process
  • Diffusion
  • Fractal
  • Large deviation
  • Sierpinski gasket

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Mathematics(all)
  • Statistics and Probability

Cite this

Large deviations for Brownian motion on the Sierpinski gasket. / Arous, Gerard Ben; Kumagai, Takashi.

In: Stochastic Processes and their Applications, Vol. 85, No. 2, 01.02.2000, p. 225-235.

Research output: Contribution to journalArticle

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