Yukawa potential, panharmonic measure and Brownian motion
Research output: Contribution to journal › Article › Scientific › peer-review
- University of Vaasa
This paper continues our earlier investigation, where a walk-on-spheres (WOS) algorithm for Monte Carlo simulation of the solutions of the Yukawa and the Helmholtz partial differential equations (PDEs) was developed by using the Duffin correspondence. In this paper, we investigate the foundations behind the algorithm for the case of the Yukawa PDE. We study the panharmonic measure, which 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.
|Publication status||Published - 1 May 2018|
|MoE publication type||A1 Journal article-refereed|
- Bessel functions, Brownian motion, Duffin correspondence, Harmonic measure, Monte Carlo simulation, Panharmonic measure, Potential theory, Walk-on-spheres algorithm, Yukawa equation