Volume 11, February 2007Special Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthday
|Page(s)||301 - 326|
|Published online||17 August 2007|
A Donsker theorem to simulate one-dimensional processes with measurable coefficients
École Nationale des Ponts et Chaussées,
6 et 8 avenue Blaise Pascal
Cité Descartes, Champs sur Marne,
77455 Marne la Vallée Cedex 2,
2 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
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.
Mathematics Subject Classification: 60J60 / 65C
Key words: Monte Carlo methods / Donsker theorem / one-dimensional process / scale function / divergence form operators / Feynman-Kac formula / elliptic PDE problem.
© EDP Sciences, SMAI, 2007
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