Computation of the local time of reflecting Brownian motion and the probabilistic representation of the Neumann problem

DOI10.4310/CMS.2017.v15.n1.a11zbMath1358.65005arXiv1502.01319MaRDI QIDQ510240

Yijing Zhou, Wei Cai, Elton P. Hsu

Publication date: 17 February 2017

Published in: Communications in Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1502.01319

zbMATH Keywords

convergenceBrownian motionnumerical testsNeumann boundary conditionLaplace equationrandom walkreflecting Brownian motionboundary local timeSkorohod problemwalk-on-spheres

Mathematics Subject Classification ID

Probabilistic methods, particle methods, etc. for boundary value problems involving PDEs (65N75) Monte Carlo methods (65C05) Sums of independent random variables; random walks (60G50) Brownian motion (60J65) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (6)

A Parallel Iterative Probabilistic Method for Mixed Problems of Laplace Equations with the Feynman--Kac Formula of Killed Brownian Motions ⋮ Numerical solution of the Robin problem of Laplace equations with a Feynman-Kac formula and reflecting Brownian motions ⋮ A numerical method for solving snapping out Brownian motion in 2D bounded domains ⋮ A path integral Monte Carlo (PIMC) method based on Feynman-Kac formula for electrical impedance tomography ⋮ What is the fractional Laplacian? A comparative review with new results ⋮ Sweetest taboo processes

Uses Software

• nanoflann
• GitHub

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