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

Pierre Étoré; Antoine Lejay

ESAIM: Probability and Statistics (2007)

  • Volume: 11, page 301-326
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Étoré, Pierre, and Lejay, Antoine. "A Donsker theorem to simulate one-dimensional processes with measurable coefficients." ESAIM: Probability and Statistics 11 (2007): 301-326. <http://eudml.org/doc/250096>.

@article{Étoré2007,
abstract = { 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. },
author = {Étoré, Pierre, Lejay, Antoine},
journal = {ESAIM: Probability and Statistics},
keywords = {Monte Carlo methods; Donsker theorem; one-dimensional process; scale function; divergence form operators; Feynman-Kac formula; elliptic PDE problem.; donsker theorem; scale function; divergence form operators; elliptic PDE problem},
language = {eng},
month = {8},
pages = {301-326},
publisher = {EDP Sciences},
title = {A Donsker theorem to simulate one-dimensional processes with measurable coefficients},
url = {http://eudml.org/doc/250096},
volume = {11},
year = {2007},
}

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
DA - 2007/8//
PB - EDP Sciences
VL - 11
SP - 301
EP - 326
AB - 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.
LA - eng
KW - Monte Carlo methods; Donsker theorem; one-dimensional process; scale function; divergence form operators; Feynman-Kac formula; elliptic PDE problem.; donsker theorem; scale function; divergence form operators; elliptic PDE problem
UR - http://eudml.org/doc/250096
ER -

References

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