UNIVERSITY
OF WROCŁAW
 
Main Page
Contents
Online First
General Information
Instructions for authors


VOLUMES
43.1 42.2 42.1 41.2 41.1 40.2 40.1
39.2 39.1 38.2 38.1 37.2 37.1 36.2
36.1 35.2 35.1 34.2 34.1 33.2 33.1
32.2 32.1 31.2 31.1 30.2 30.1 29.2
29.1 28.2 28.1 27.2 27.1 26.2 26.1
25.2 25.1 24.2 24.1 23.2 23.1 22.2
22.1 21.2 21.1 20.2 20.1 19.2 19.1
18.2 18.1 17.2 17.1 16.2 16.1 15
14.2 14.1 13.2 13.1 12.2 12.1 11.2
11.1 10.2 10.1 9.2 9.1 8 7.2
7.1 6.2 6.1 5.2 5.1 4.2 4.1
3.2 3.1 2.2 2.1 1.2 1.1
 
 
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.

Download:    Abstract    Full text   Abstract + References