Estimates of the transition densities for the reflected Brownian motion on simple nested fractals

Abstract

We give sharp two-sided estimates for the functions gMt, x, y and gMt, x, y − gt, x, y, where gMt, x, y are the transition probability densities of the reflected Brownian motion on an Mcomplex of order M ∈ Z of an unbounded planar simple nested fractal and gt, x, y are the transition probability densities of the “free” Brownian motion on this fractal. This is done for a large class of planar simple nested fractals with the good labeling property.