The Simplest Random Walks for the Dirichlet Problem

DOI10.1137/S0040585X97979433zbMath1038.60066OpenAlexW2027729994MaRDI QIDQ4442886

M. V. Tretyakov, Grigori N. Milstein

Publication date: 21 January 2004

Published in: Theory of Probability & Its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s0040585x97979433

zbMATH Keywords

Dirichlet problemMarkov chainsrandom walksstochastic differential equationselliptic equationsparabolic equationsprobabilistic representationweak approximations of solutions of stochastic differential equations

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Diffusion processes (60J60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Numerical methods for partial differential equations, boundary value problems (65N99)

Related Items (5)

Random walk algorithm for the Dirichlet problem for parabolic integro-differential equation ⋮ Applications of some formulas for finite Markov chains ⋮ A posteriori error analysis and adaptivity for high-dimensional elliptic and parabolic boundary value problems ⋮ Simplest random walk for approximating Robin boundary value problems and ergodic limits of reflected diffusions ⋮ Solving the Dirichlet problem for Navier-Stokes equations by probabilistic approach

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