| Issue |
ESAIM: PS
Volume 11, February 2007
Special Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthday
|
|
|---|---|---|
| Page(s) | 236 - 247 | |
| DOI | https://doi.org/10.1051/ps:2007018 | |
| 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
Received:
3
April
2006
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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