Authors: E. Csáki 1 and Y. Hu 2
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  • 1 Hungarian Academy of Sciences A. Rényi Institute of Mathematics Reáltanoda u. 13-15 P.O.B. 127 Budapest H-1364 Hungary Reáltanoda u. 13-15 P.O.B. 127 Budapest H-1364 Hungary
  • 2 University Paris XIII Département de Mathématiques, Institut Galilée (L.A.G.A. UMR 7539) 99 Avenue J-B Clément 93430 Villetaneuse France 99 Avenue J-B Clément 93430 Villetaneuse France
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Abstract  

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 L2-norm estimates between the Wiener sausage and the Brownian intersection local times.

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