Behavior of the Euler scheme with decreasing step in a degenerate situation
ESAIM: Probability and Statistics, Tome 11 (2007), pp. 236-247.

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.

DOI : 10.1051/ps:2007018
Classification : 60H10, 65C30, 37M25
Mots clés : one-dimensional diffusion process, degenerate coefficient, invariant measure, Euler scheme 
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Lemaire, Vincent. Behavior of the Euler scheme with decreasing step in a degenerate situation. ESAIM: Probability and Statistics, Tome 11 (2007), pp. 236-247. doi : 10.1051/ps:2007018. http://archive.numdam.org/articles/10.1051/ps:2007018/

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