Geodesic
A Donsker theorem to simulate one-dimensional processes with measurable coefficients
ESAIM: Probability and Statistics, Tome 11 (2007), pp. 301-326

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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.

DOI : 10.1051/ps:2007021
Classification : 60J60, 65C
Keywords: Monte Carlo methods, Donsker theorem, one-dimensional process, scale function, divergence form operators, Feynman-Kac formula, elliptic PDE problem 
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     author = {\'Etor\'e, Pierre and Lejay, Antoine},
     title = {A {Donsker} theorem to simulate one-dimensional processes with measurable coefficients},
     journal = {ESAIM: Probability and Statistics},
     pages = {301--326},
     publisher = {EDP-Sciences},
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     year = {2007},
     doi = {10.1051/ps:2007021},
     mrnumber = {2339295},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps:2007021/}
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Étoré, Pierre; Lejay, Antoine. A Donsker theorem to simulate one-dimensional processes with measurable coefficients. ESAIM: Probability and Statistics, Tome 11 (2007), pp. 301-326. doi: 10.1051/ps:2007021

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