Strong approximations of three-dimensional Wiener sausages |
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| Authors: | E Csáki Y Hu |
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| Institution: | (1) A. Rényi Institute of Mathematics, Hungarian Academy of Sciences, Reáltanoda u. 13-15, P.O.B. 127, Budapest, H-1364, Hungary;(2) Département de Mathématiques, Institut Galilée (L.A.G.A. UMR 7539), University Paris XIII, 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 L
2-norm estimates between the Wiener sausage and the Brownian intersection local times.
Research supported by the Hungarian National Foundation for Scientific Research, Grants T 037886, T 043037 and K 61052. |
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| Keywords: | Wiener sausage intersection local times strong approximation |
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