no. 3-4
Probability Theory
The Neyman–Pearson lemma under g-probability
[Lemme de Neyman–Pearson généralisé pour les g-espérances]

Présenté par : Paul Deheuvels

Ji, Shaolin1 ; Zhou, Xun Yu2, 3
1 School of Mathematics and System Sciences, Shandong University, Jinan, Shandong, 250100, PR China
2 Mathematical Institute, University of Oxford, 24–29 St Giles, Oxford OX1 3LB, UK
3 Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong
Comptes Rendus. Mathématique, Tome 346 (2008) no. 3-4, pp. 209-212.

Le lemme fondamental de Neyman–Pearson est généralisé au cas de g-probabilités. Sous des hypothèses de convexité, une condition suffisante et nécessaire caractérisant le test randomisé optimal est obtenue au moyen du principe du maximum dans le cadre du contrôle stochastique.

The Neyman–Pearson fundamental lemma is generalized under g-probability. With convexity assumptions, a sufficient and necessary condition which characterizes the optimal randomized tests is obtained via a maximum principle for stochastic control.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.12.007
Ji, Shaolin 1 ; Zhou, Xun Yu 2, 3

1 School of Mathematics and System Sciences, Shandong University, Jinan, Shandong, 250100, PR China
2 Mathematical Institute, University of Oxford, 24–29 St Giles, Oxford OX1 3LB, UK
3 Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong 
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Ji, Shaolin; Zhou, Xun Yu. The Neyman–Pearson lemma under g-probability. Comptes Rendus. Mathématique, Tome 346 (2008) no. 3-4, pp. 209-212. doi : 10.1016/j.crma.2007.12.007. http://www.numdam.org/articles/10.1016/j.crma.2007.12.007/

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Cité par Sources :

⁎ The authors thank the partial support from the National Basic Research Program of China (973 Program, No. 2007CB814900), the RGC Earmark Grant No. 418606, and a start-up fund at Oxford.

⁎⁎ This Note is the succinct version of a text on file for five years in the Academy Archives.