A Donsker theorem to simulate one-dimensional processes with measurable coefficients

Pierre Étoré; Antoine Lejay

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Probabilistic interpretation and random walk on spheres algorithms for the Poisson-Boltzmann equation in molecular dynamics

Mireille Bossy, Nicolas Champagnat, Sylvain Maire, Denis Talay (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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Motivated by the development of efficient Monte Carlo methods for PDE models in molecular dynamics, we establish a new probabilistic interpretation of a family of divergence form operators with discontinuous coefficients at the interface of two open subsets of $ℝ^{d}$ . This family of operators includes the case of the linearized Poisson-Boltzmann equation used to compute the electrostatic free energy of a molecule. More precisely, we explicitly construct a Markov process whose infinitesimal...