Pitman, Jim; Yor, Marc Asymptotic laws of planar Brownian motion. (English) Zbl 0607.60070 Ann. Probab. 14, 733-779 (1986). 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 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. Reviewer: J.F.Le Gall Cited in 2 ReviewsCited in 46 Documents MSC: 60J65 Brownian motion 60J55 Local time and additive functionals 60F05 Central limit and other weak theorems 60H05 Stochastic integrals 60G44 Martingales with continuous parameter Keywords:planar Brownian motion; additive functionals; windings about points of the plane; Knight’s theorem Citations:Zbl 0089.136 PDF BibTeX XML Cite \textit{J. Pitman} and \textit{M. Yor}, Ann. Probab. 14, 733--779 (1986; Zbl 0607.60070) Full Text: DOI OpenURL