FUNCTIONAL ITERATIONS AND STOPPING-TIMES FOR BROWNIAN-MOTION ON THE SIERPINSKI GASKET

We investigate the distribution of the hitting time T defined by the f irst visit of the Brownian motion on the Sierpinski gasket at geodesic distance r from the origin. For this purpose we perform a precise ana lysis of the moment generating function of the random variable T. The key result is an explicit description of the analytic behaviour of the Laplace-Stieltjes transform of the distribution function of T. This y ields a series expansion for the distribution function and the asympto tics for t --> 0.