Estimates of transition densities for Brownian motion of 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, Hölder order of the resolvent densities, sample paths and local times are obtained. The results are obtained by using the theory of multi-type branching processes.
transition densities of Brownian motion on nested fractals
scientific article; zbMATH DE number 569088