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Large deviations for Brownian motion on the Sierpinski gasket

Author

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  • Arous, Gerard Ben
  • Kumagai, Takashi

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 [var epsilon]-->0, we prove that the large deviations hold for as n-->[infinity] using one parameter family of rate functions . As a corollary, we obtain Strassen-type laws of the iterated logarithm.

Suggested Citation

  • Arous, Gerard Ben & Kumagai, Takashi, 2000. "Large deviations for Brownian motion on the Sierpinski gasket," Stochastic Processes and their Applications, Elsevier, vol. 85(2), pages 225-235, February.
    • Handle: RePEc:eee:spapps:v:85:y:2000:i:2:p:225-235
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    Cited by:

    1. Hideaki Noda, 2017. "Large Deviations for Brownian Motion on Scale Irregular Sierpinski Gaskets," Journal of Theoretical Probability, Springer, vol. 30(3), pages 852-875, September.
    2. Toshiro Watanabe, 2002. "Shift Self-Similar Additive Random Sequences Associated with Supercritical Branching Processes," Journal of Theoretical Probability, Springer, vol. 15(3), pages 631-665, July.

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