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Behavior of the Euler scheme with decreasing stepin a degenerate situation

Published online by Cambridge University Press:  19 June 2007

Vincent Lemaire
Vincent Lemaire*
Affiliation:
Laboratoire d'Analyse et de Mathématiques Appliquées, UMR 8050, Université de Marne-la-Vallée, 5 boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée Cedex 2, France; Vincent.Lemaire@univ-mlv.fr
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Abstract

The aim of this short note is to study the behavior of the weighted empirical measures of the decreasing step Euler scheme of a one-dimensional diffusion process having multiple invariant measures. This situation can occur when the drift and the diffusion coefficient are vanish simultaneously.

Keywords

One-dimensional diffusion processdegenerate coefficientinvariant measureEuler scheme.

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