ESTIMATES OF TRANSITION DENSITIES FOR BROWNIAN-MOTION ON NESTED FRACTALS

We obtain upper and lower bounds for the transition densities of Brownian motion on nested fractals. Compared with the estimate on the Sierpinski gasket, the results require the introduction of a new exponent, d(J), related to the ''shortest path metric'' and ''chemical exponent'' on nested fractals. Further, Holder order of the resolvent densities, sample paths and local times are obtained. The results are obtained using the theory of multi-type branching processes.