Comptes Rendus
no. 7
Statistics/Probability Theory
Fluctuation of stochastic systems with average equilibrium point
[Fluctuation des systèmes stochastiques avec point d'équilibre en moyenne]

Présenté par : Paul Deheuvels

Yaroslav Chabaniuk1 ; Vladimir S. Koroliuk2 ; Nikolaos Limnios3
1 Applied Mathematics Department, University of Technology of Lviv, 79013 Lviv, Ukraine
2 Ukrainian National Academy of Science, 01601 Kiev 4, Ukraine
3 LMAC/GI, Université de technologie de Compiègne, BP 20529, 60206 Compiègne, France
Comptes Rendus. Mathématique, Volume 345 (2007) no. 7, pp. 405-410.

Cette Note concerne l'approximation de diffusion des systèmes dynamiques où la fonction de vitesse contient un terme de perturbation. Ainsi le problème considéré est l'étude de la fluctuation du système initial par rapport au terme de perturbation.

This Note deals with the diffusion approximation of dynamical systems where the velocity function contains a perturbing term. Thus, the problem considered is the investigation of the fluctuation of the initial system with respect to the above perturbing term.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.07.029
Yaroslav Chabaniuk 1 ; Vladimir S. Koroliuk 2 ; Nikolaos Limnios 3

1 Applied Mathematics Department, University of Technology of Lviv, 79013 Lviv, Ukraine
2 Ukrainian National Academy of Science, 01601 Kiev 4, Ukraine
3 LMAC/GI, Université de technologie de Compiègne, BP 20529, 60206 Compiègne, France 
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     title = {Fluctuation of stochastic systems with average equilibrium point},
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     pages = {405--410},
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Yaroslav Chabaniuk; Vladimir S. Koroliuk; Nikolaos Limnios. Fluctuation of stochastic systems with average equilibrium point. Comptes Rendus. Mathématique, Volume 345 (2007) no. 7, pp. 405-410. doi : 10.1016/j.crma.2007.07.029. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.07.029/

[1] V.S. Koroliuk; N. Limnios Stochastic Systems in Merging Phase Space, World Scientific, 2005

[2] L. Ljung; G. Pflung; H. Walk Stochastic Approximation and Optimization of Random Systems, Birkhäuser Verlag, Basel, 1992

[3] M.B. Nevelson; R.Z. Khasminsky Stochastic Approximation and Recurrent Estimation, Nauka, Moscow, 1972

[4] A.V. Skorokhod; F.C. Hoppensteadt; H. Salehi Random Perturbation Method with Application in Science and Engineering, Springer, 2002

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