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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 39, Fasc. 10,
pages 423 - 440
DOI: 10.19195/0208-4147.39.2.10
 

ESTIMATES OF THE TRANSITION DENSITIES FOR THE REFLECTED BROWNIAN MOTION ON SIMPLE NESTED FRACTALS

Mariusz Olszewski

Abstract: We give sharp two-sided estimates for the functions g (t,x,y) M and g (t,x,y)- g(t,x,y) M , where g (t,x,y) M are the transition probability densities of the reflected Brownian motion on an M -complex of order M ∈ ℤ of an unbounded planar simple nested fractal and g(t,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.

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.

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