HAL : inria-00077851, version 1

DOI : 10.1051/ps:2007021

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ESAIM: Probability and Statistics 11 (2007) 301-326

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

Pierre Etoré 1, 2, Antoine Lejay 1, 2

(2007)

In this paper, we prove a Donker 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.

1 :	OMEGA (INRIA Sophia Antipolis / INRIA Lorraine / IECN)
	CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II
2 :	Institut Elie Cartan Nancy (IECN)
	CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine

Domaine

:

Mathématiques/Probabilités

Mots-clés : Monte Carlo methods – Donsker theorem – one-dimensional process – scale function – divergence form operators – Feynman-Kac formula – elliptic PDE problem

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Contributeur : Antoine Lejay <>

Soumis le : Jeudi 1 Juin 2006, 13:51:21

Dernière modification le : Lundi 1 Octobre 2007, 14:58:21