ESTIMATES OF THE TRANSITION DENSITIES FOR THE REFLECTED
BROWNIAN MOTION ON SIMPLE NESTED FRACTALS
Abstract: We give sharp two-sided estimates for the functions
and
, where
are the transition probability densities of the
reflected Brownian motion on an
-complex of order
of an unbounded planar
simple nested fractal and
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.
2000 AMS Mathematics Subject Classification: Primary: 60J35, 28A80; Secondary:
60J25, 60J65.
Keywords and phrases: Projection, good labeling property, reflected process, transition
probability density, simple nested fractal, graph metric, Sierpiński gasket.