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arXiv · 2607.10528

Walk-on-Cubes Monte Carlo Simulation for nonisotropic fractional Laplace, Helmholtz, and Yukawa equations

Antti Rasila·Tommi Sottinen·Yaotong Yuan
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Abstract

We study the nonisotropic fractional analogs of Laplace, Helmholtz and Yukawa equations. We provide a Duffin correspondence for the Yukawa equation and a Feynman--Kac reconstruction for the Helmholtz equation. The foundation of our analysis is the fact that the nonisotropic fractional Laplace equation is related to a symmetric $\alpha$-stable L\'evy process with independent identically distributed components. By using this relation we provide a Walk-on-Cubes algorithm that simulates the solutions of Helmholtz and Yukawa equations.

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BibTeXRIS

Antti Rasila, Tommi Sottinen, Yaotong Yuan. 2026-07-12. Walk-on-Cubes Monte Carlo Simulation for nonisotropic fractional Laplace, Helmholtz, and Yukawa equations. https://arxiv.org/abs/2607.10528

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