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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References
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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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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