Homogenization of nested fractals (Q1912571)

We study the homogenization problem on nested fractals. Let \(X_t\) be the continuous time Markov chain on the pre-nested fractal given by putting i.i.d. random resistors on each cell. It is proved that under some conditions, \(\alpha^{-n} X_{t^n_E t}\) converges in law to a constant time change of the Brownian motion on the fractal as \(n\to \infty\), where \(\alpha\) is the contraction rate and \(t_E\) 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.