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On the law of the iterated logarithm for Brownian motion on compact manifolds

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Abstract

By taking a functional analytic point of view, we consider a family of distributions (continuous linear functionals on smooth functions), denoted by {μt, t > 0}, associated to the law of the iterated logarithm for Brownian motion on a compact manifold. We give a complete characterization of the collection of limiting distributions of {μt; t > 0}.

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Acknowledgements

This work was supported by Collaboration Grants for Mathematicians of the Simons Foundation (Grant No. 355480). The authors thank the anonymous referees for their careful reading of the paper and for their numerous suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL, 60607, USA

    Cheng Ouyang & Jennifer Pajda-De La O

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  1. Cheng Ouyang
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  2. Jennifer Pajda-De La O
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Correspondence to Cheng Ouyang.

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In Memory of Professor Kai Lai Chung on the 100th Anniversary of His Birth

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Ouyang, C., Pajda-De La O, J. On the law of the iterated logarithm for Brownian motion on compact manifolds. Sci. China Math. 62, 1511–1518 (2019). https://doi.org/10.1007/s11425-017-9417-1

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  • DOI: https://doi.org/10.1007/s11425-017-9417-1

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