Optimal Bounds for Cauchy Approximations for the Winding Distribution of Planar Brownian Motion |
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| Authors: | V. Bentkus G. Pap M. Yor |
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| Affiliation: | (1) Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania;(2) Laboratoire de Probabilités, CNRS URA 224, Université Paris VI, 4, Place Jussieu, Tour 56, 3° étage, F-75252 Paris Cedex 05, France |
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| Abstract: | Optimal nonuniform bounds are given for the remainder terms in Spitzer's theorem, which gives some final answer to the question of Cauchy approximations for the winding distribution of planar Brownian motion. As a corollary, a large deviation result is presented. Optimal nonuniform bounds for the approximations of the density are also derived. |
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| Keywords: | planar Brownian motion Spitzer's theorem nonuniform asymptotic expansions of distribution functions |
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