Large deviations for Brownian motion on the Sierpinski gasket

Gerard Ben Arous*, Takashi Kumagai

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


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 εnz≡(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
Pages (from-to)225-235
Number of pages11
JournalStochastic Processes and their Applications
Issue number2
Publication statusPublished - 2000 Feb 1
Externally publishedYes


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

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics


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