Large deviations for Brownian motion on the Sierpinski gasket

We study large deviations for Brownian motion on the Sierpinski gasket in t he short time limit. Because of the subtle oscillation of hitting times of the process, no large deviation principle can hold. In fact, our result sho ws that there is an infinity of different large deviation principles for di fferent subsequences, with different (good) rate functions. Thus, instead o f taking the time scaling epsilon --> 0, we prove that the large deviations hold for E-n(z) = (2/5)(n)z as n --> infinity, using one parameter family of rate functions I-z (z is an element of [2/5, 1)). As a corollary, we obt ain Strassen-type laws of the iterated logarithm. (C) 2000 Elsevier Science B.V. All rights reserved. MSG. 60F10; 60J60; 60J80.