Abstract

Our method of proof relies upon the skew–product representation of planar Brownian motion, and changes of probabilities between the laws of Bessel processes, as indicated in [8], [9], [10]; in particular, this paper is an improvement of [10], which discusses only the case k = 2. The spirit of our expansion is close to the Edgeworth type expansions in the central limit theorems, that is, to the asymptotic expansions of the distribution

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