Initial-boundary value problem for the heat equation -- a stochastic algorithm

DOI10.1214/17-AAP1348zbMath1397.35119arXiv1610.03963OpenAlexW2532982383MaRDI QIDQ1661575

Madalina Deaconu, Samuel Herrmann

Publication date: 16 August 2018

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.03963

zbMATH Keywords

heat equationinitial-boundary value problemrandomized algorithmrandom walkRiesz potentialsubmartingalemean-value formulaheat balls

Mathematics Subject Classification ID

Computational methods in Markov chains (60J22) Martingales with discrete parameter (60G42) Monte Carlo methods (65C05) Initial-boundary value problems for second-order parabolic equations (35K20)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Hitting time for Bessel processes-walk on moving spheres algorithm (WoMS)
• Some evaluations for continuous Monte Carlo method by using Brownian hitting process
• Mean property for the heat-conduction equation
• \(\varepsilon\)-shell error analysis for ``walk on spheres algorithms
• On the Dirichlet problem
• The rate of convergence of the walk on spheres algorithm
• The walk on moving spheres: a new tool for simulating Brownian motion's exit time from a domain
• Simulation of hitting times for Bessel processes with non-integer dimension
• Maggioranti e minoranti delle soluzioni delle equazioni paraboliche
• Spherical and Plane Integral Operators for PDEs
• Some Continuous Monte Carlo Methods for the Dirichlet Problem
• Diffusions and Elliptic Operators
• The Floating Random Walk and Its Application to Monte Carlo Solutions of Heat Equations
• A Mean Value Theorem for the Heat Equation
• Stochastic differential equations. An introduction with applications.