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

Published online by Cambridge University Press:  17 August 2007

Pierre Étoré  and
Antoine Lejay
Pierre Étoré
Affiliation:
CERMICS, École Nationale des Ponts et Chaussées, 6 et 8 avenue Blaise Pascal Cité Descartes, Champs sur Marne, 77455 Marne la Vallée Cedex 2, France; Pierre.Etore@cermics.enpc.fr
Antoine Lejay
Affiliation:
Projet OMEGA, Institut Élie Cartan (UMR 7502, Nancy-Université, CNRS, INRIA) and INRIA Lorraine, Campus scientifique, BP 239, 54506 Vandoeuvre-lès-Nancy Cedex, France; Antoine.Lejay@iecn.u-nancy.fr
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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.

Keywords

Monte Carlo methodsDonsker theoremone-dimensional processscale functiondivergence form operatorsFeynman-Kac formulaelliptic PDE problem.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 11: Special Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthdaySpecial Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthday , June 2007 , pp. 301 - 326
Copyright
© EDP Sciences, SMAI, 2007

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