Excursions in a cone for two-dimensional Brownian motion (Q1068444)

Let \(\{B(t),0\leq t<\infty \}\) be the two-dimensional standard Brownian motion process with continuous paths on a probability space. A most significant property of the Brownian paths is known as the winding property: Let T be a finite Markov time of the two-dimensional Brownian motion process, then with probability one \(\{B(t),T\leq t<T+\epsilon \}\) winds about B(T) and cuts itself for every \(\epsilon >0\). In this paper we will consider the contrary. Namely, when does occur a non-winding in the two-dimensional Brownian paths? We also determine the law of a non- winding part by giving the corresponding conditioned limit theorem for the Brownian motion.