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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; [email protected]
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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.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 11: Special Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthdaySpecial Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthday , June 2007 , pp. 236 - 247
Copyright
© EDP Sciences, SMAI, 2007

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References

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