Yukawa Potential, Panharmonic Measure and Brownian Motion
Complex Variables
2016-06-17 v3 Analysis of PDEs
Probability
Abstract
In [25] a Walk On Spheres (WOS) algorithm for Monte Carlo simulation of the solutions of the Yukawa and the Helmholtz PDE's was developed by using the so-called Duffin correspondence. In this paper we investigate the foundations behind the algorithm for the case of the Yukawa PDE. We study the panharmonic measure that is a generalization of the harmonic measure for the Yukawa PDE. We show that there are natural stochastic definitions for the panharmonic measure in terms of the Brownian motion and that the harmonic and the panharmonic measures are all mutually equivalent. Furthermore, we calculate their Radon--Nikodym derivatives explicitly for some balls, which is a key result behind the WOS algorithm.
Keywords
Cite
@article{arxiv.1310.2167,
title = {Yukawa Potential, Panharmonic Measure and Brownian Motion},
author = {Antti Rasila and Tommi Sottinen},
journal= {arXiv preprint arXiv:1310.2167},
year = {2016}
}
Comments
15 pages, 1 figure