Abstract. Let $B(t)$, $X(t)$ and $Y(t)$ be independent standard 1d Brownian motions. Define $X^+(t)$ and $Y^-(t)$ as the trajectories of the processes $X(t)$ and $Y(t)$ pushed upwards and, respectively, downwards by $B(t)$, according to Skorohod-reflection. In the recent paper [8], Jon Warren proves inter alia that $Z(t):= X^+(t)-Y^-(t)$ is a three-dimensional Bessel-process. In this note, we present an alternative, elementary proof of this fact.

AMS Subject Classification (1991): 60J65

Keyword(s): Brownian motion, Skorohod reflection, Bessel process

Received September 8, 2007. (Registered under 6461/2009.)