Large deviations for Brownian motion on the Sierpinski gasket

We study large deviations for Brownian motion on the Sierpinski gasket in the short time limit. Because of the subtle oscillation of hitting times of the process, no large deviation principle can hold. In fact, our result shows that there is an infinity of different large deviation principles for different subsequences, with different (good) rate functions. Thus, instead of taking the time scaling ε→0, we prove that the large deviations hold for εnz≡(25)nz as n→∞ using one parameter family of rate functions Iz (z∈[25,1)). As a corollary, we obtain Strassen-type laws of the iterated logarithm.