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, dJ, related to the "shortest path metric" and "chemical exponent" on nested fractals. Further, Hölder order of the resolvent densities, sample paths and local times are obtained. The results are obtained using the theory of multi-type branching processes.
- Mathematics Subject Classification: 60J60, 60J65, 60J80
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty