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Large Deviations for Brownian Motion on Scale Irregular Sierpinski Gaskets

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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.

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Acknowledgments

This work is the part of author’s Ph.D. thesis under the supervision of Professor S. Kusuoka. The author would like to thank him for his valuable suggestions, helpful comments and encouragements. Also the author would like to thank anonymous referees for valuable comments and suggestions that have improved this paper.

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  1. Sumitomo Mitsui Banking Corporation, 1-1-2, Marunouchi, Chiyoda-ku, Tokyo, Japan

    Hideaki Noda

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  1. Hideaki Noda
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Correspondence to Hideaki Noda.

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Noda, H. Large Deviations for Brownian Motion on Scale Irregular Sierpinski Gaskets. J Theor Probab 30, 852–875 (2017). https://doi.org/10.1007/s10959-016-0682-8

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  • DOI: https://doi.org/10.1007/s10959-016-0682-8

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