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arXiv · 1804.04998

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

Mariusz Olszewski
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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 $M \in \mathbb{Z}$ 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.

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Mariusz Olszewski. 2018-04-13. Estimates of the transition densities for the reflected Brownian motion on simple nested fractals. https://arxiv.org/abs/1804.04998

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