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

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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
Keywords: one-dimensional diffusion process, degenerate coefficient, invariant measure, Euler scheme 
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     author = {Lemaire, Vincent},
     title = {Behavior of the {Euler} scheme with decreasing step in a degenerate situation},
     journal = {ESAIM: Probability and Statistics},
     pages = {236--247},
     publisher = {EDP-Sciences},
     volume = {11},
     year = {2007},
     doi = {10.1051/ps:2007018},
     mrnumber = {2320818},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps:2007018/}
}
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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

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