Volume 11, February 2007Special Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthday
|Page(s)||236 - 247|
|Published online||19 June 2007|
Behavior of the Euler scheme with decreasing step in a degenerate situation
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
Revised: 16 October 2006
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.
Mathematics Subject Classification: 60H10 / 65C30 / 37M25
Key words: One-dimensional diffusion process / degenerate coefficient / invariant measure / Euler scheme.
© EDP Sciences, SMAI, 2007
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