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Solving Wentzell-Dirichlet Boundary Value Problem with Superabundant Data Using Reflecting Random Walk Simulation

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  • J.-P. Morillon

    (Université de La Réunion)

Abstract

In this paper, we are interested in numerical solution of some linear boundary value problems with Wentzell’s boundary part and superabundant data on this part, by the means of simulation of reflected random walks. We use a probabilistic interpretation of solution, assuming that the diffusion coefficient and the boundary data are sufficiently smooth, and applying Itô’s formula. From this stochastic representation of solution, we extend the algorithm obtained for mixed standard boundary conditions to the case of diffusion-reflection on the boundary, so called Wentzell’s boundary condition. We then obtain numerical results by applying the stochastic method based upon this generalized algorithm.

Suggested Citation

  • J.-P. Morillon, 2015. "Solving Wentzell-Dirichlet Boundary Value Problem with Superabundant Data Using Reflecting Random Walk Simulation," Methodology and Computing in Applied Probability, Springer, vol. 17(3), pages 697-719, September.
    • Handle: RePEc:spr:metcap:v:17:y:2015:i:3:d:10.1007_s11009-013-9390-3
    DOI: 10.1007/s11009-013-9390-3
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    References listed on IDEAS

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    1. Souza de Cursi, J.E., 1994. "Numerical methods for linear boundary value problems based on Feyman–Kac representations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 36(1), pages 1-16.
    2. Bally, Vlad & Talay, Denis, 1995. "The Euler scheme for stochastic differential equations: error analysis with Malliavin calculus," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 38(1), pages 35-41.
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