an:03932119
Zbl 0582.60048
Shimura, Michio
Excursions in a cone for two-dimensional Brownian motion
EN
J. Math. Kyoto Univ. 25, 433-443 (1985).
00150667
1985
j
60G17 60J65 60F15
winding property; non-winding in the two-dimensional Brownian; conditioned limit theorem
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.