Upper functions for plane Brownian windings (Q1283377)

The author presents sharp results on the upper functions for the windings of planar Brownian motion. He considers total windings, big windings and windings in an annulus. The proofs are based on the skew-product representation of planar Brownian motion and introduce some Borel-Cantelli-type lemmas for certain dependent events. The results obtained complement those of \textit{J. Bertoin} and \textit{W. Werner} [in: Séminaire de Probabilités XXVIII. Lect. Notes Math. 1583, 164-171 (1994; Zbl 0810.60077)], \textit{Z. Shi} [in: ibid., 122-137 (1994; Zbl 0810.60076)] and in particular the recent results of \textit{Z. Shi} [Ann. Probab. 26, 112-131 (1998)].