Strong approximations of three-dimensional Wiener sausages
نویسندگان
چکیده
In this paper 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]’s fine L-norm estimates between the Wiener sausage and the Brownian intersection local times.
منابع مشابه
Moderate deviations and laws of the iterated logarithm for the volume of the intersections of Wiener sausages
Using the high moment method and the Feynman-Kac semigroup technique, we obtain moderate deviations and laws of the iterated logarithm for the volume of the intersections of two and three dimensional Wiener sausages.
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