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

Mariusz Olszewski

paper

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

arXiv:1804.04998

Abstract

We give sharp two-sided estimates for the functions $g_{M} (t, x, y)$ and $g_{M} (t, x, y) - g (t, x, y)$ , where $g_{M} (t, x, y)$ are the transition probability densities of the reflected Brownian motion on a $M$ -complex of size $M \in Z$ 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.