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We prove that the centered three-dimensional Wiener sausage can be strongly approximated by a one-dimensional Brownian motion running at a suitable time clock. The strong approximation gives all possible laws of iterated logarithm as well as the convergence in law in terms of process for the normalized Wiener sausage. The proof relies on Le Gall [10]șs fine L 2-norm estimates between the Wiener sausage and the Brownian intersection local times.

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Periodica Mathematica Hungarica
G. Pollák
E. Csáki
, and
Z. Magyar
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We present a joint functional iterated logarithm law for the Wiener process and the principal value of its local times.

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