Probabilistic methods for finite difference approximations to degenerate elliptic and parabolic equations with Neumann and Dirichlet boundary conditions

DOI10.1016/0022-247X(76)90097-4zbMath0329.65055MaRDI QIDQ1227269

Harold J. Kushner

Publication date: 1976

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Boundary value problems for second-order elliptic equations (35J25) Initial-boundary value problems for second-order parabolic equations (35K20) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite difference methods for boundary value problems involving PDEs (65N06) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

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Continuous-time Random Walks for the Numerical Solution of Stochastic Differential Equations ⋮ Solving Wentzell-Dirichlet boundary value problem with superabundant data using reflecting random walk simulation ⋮ SPECTRWM: Spectral Random Walk Method for the Numerical Solution of Stochastic Partial Differential Equations ⋮ Sticky Brownian Motion and Its Numerical Solution ⋮ Stochastic methods for Dirichlet problems

Cites Work

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• Probability methods for the convergence of finite difference approximations to partial differential equations
• The approximate calculation of invariant measures of diffusions via finite difference approximations to degenerate elliptic partial differential equations
• Finite difference methods for the weak solutions of the Kolmogorov equation for the density of both diffusion and conditional diffusion processes
• Approximations, existence, and numerical procedures for optimal stochastic controls
• Probability limit theorems and the convergence of finite difference approximations of partial differential equations
• Diffusion processes with boundary conditions

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