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

Mireille Bossy; Nicolas Champagnat; Sylvain Maire; Denis Talay

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

Pierre Étoré, Antoine Lejay (2007)

ESAIM: Probability and Statistics

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In this paper, we prove a Donsker theorem for one-dimensional processes generated by an operator with measurable coefficients. We construct a random walk on any grid on the state space, using the transition probabilities of the approximated process, and the conditional average times it spends on each cell of the grid. Indeed we can compute these quantities by solving some suitable elliptic PDE problems.