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Large Deviations for Brownian Motion on Scale Irregular Sierpinski Gaskets

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  • Hideaki Noda

    (Sumitomo Mitsui Banking Corporation)

Abstract

We study sample path large deviation principles for Brownian motion on scale irregular Sierpinski gaskets which are spatially homogeneous but do not have any exact self-similarity. One notable point of our study is that the rate function depends on a large deviation parameter and as such, we can only obtain an example of large deviations in an incomplete form. Instead of showing the large deviations principle we would expect to hold true, we show Varadhan’s integral lemma and exponential tightness by using an incomplete version of such large deviations.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jotpro:v:30:y:2017:i:3:d:10.1007_s10959-016-0682-8
    DOI: 10.1007/s10959-016-0682-8
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    References listed on IDEAS

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    1. 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.
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