Homogenization on nested fractals

Summary We study the homogenization problem on nested fractals. LetX _t be the continuous time Markov chain on the pre-nested fractal given by puttingi.i.d. random resistors on each cell. It is proved that under some conditions, converges in law to a constant time change of the Brownian motion on the fractal asn, where is the contraction rate andt _E is a time scale constant. As the Brownian motion on fractals is not a semi-martingale, we need a different approach from the well-developed martingale method.Dedicated to Professor Masatoshi Fukushima on his 60th birthdayResearch partially supported by the Yukawa Foundation