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.
Classification : 60J60, 65C
Mots clés : Monte Carlo methods, Donsker theorem, one-dimensional process, scale function, divergence form operators, Feynman-Kac formula, elliptic PDE problem
@article{PS_2007__11__301_0,
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},
volume = {11},
year = {2007},
doi = {10.1051/ps:2007021},
mrnumber = {2339295},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ps:2007021/}
}
TY - JOUR AU - Étoré, Pierre AU - Lejay, Antoine TI - A Donsker theorem to simulate one-dimensional processes with measurable coefficients JO - ESAIM: Probability and Statistics PY - 2007 DA - 2007/// SP - 301 EP - 326 VL - 11 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps:2007021/ UR - https://www.ams.org/mathscinet-getitem?mr=2339295 UR - https://doi.org/10.1051/ps:2007021 DO - 10.1051/ps:2007021 LA - en ID - PS_2007__11__301_0 ER -
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. http://archive.numdam.org/articles/10.1051/ps:2007021/
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