Asymptotic laws of planar Brownian motion
This paper presents a unified approach to various asymptotic results for planar Brownian motion, involving such objects as additive functionals or windings about points of the plane. In particular, the authors obtain the joint asymptotic law of the windings about several points of the plane, thus extending a result due to \textit{F. Spitzer} [Trans. Am. Math. Soc. 87, 187-197 (1958; Zbl 0089.136)] in the case of a single point. The main tools are stochastic calculus, especially Knight's theorem on orthogonal continuous martingales, and excursion theory. A very important role is also played by the representation of planar Brownian motion in polar coordinates (the so-called skew-product representation), which is used simultaneously with several different origins.
scientific article; zbMATH DE number 3982212