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

Pierre Etoré 1, 2 Antoine Lejay 1, 2
1 OMEGA - Probabilistic numerical methods
CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, CNRS - Centre National de la Recherche Scientifique : UMR7502
Abstract : In this paper, we prove a Donker 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.
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Pierre Etoré, Antoine Lejay. A Donsker theorem to simulate one-dimensional processes with measurable coefficients. ESAIM: Probability and Statistics, EDP Sciences, 2007, 11, pp.301-326. ⟨10.1051/ps:2007021⟩. ⟨inria-00077851⟩

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