no. 3
Statistics/Probability Theory
On the stability and causality of general time-dependent bilinear models
[Sur la stabilité et la causalité des modèles bilinéaires généraux à coefficients dépendant du temps]

Présenté par : Paul Deheuvels

Bibi, Abdelouahab1
1 Département de mathématiques, laboratoire de mathématiques appliquées et modélisation, Université Mentouri, Constantine, Algeria
Comptes Rendus. Mathématique, Tome 338 (2004) no. 3, pp. 245-248.

Dans cette Note, nous donnons des conditions suffisantes d'existence et d'unicité de solution causale et stable pour la classe générale de modèles bilinéaires à coefficients dépendant du temps.

In this Note, sufficient conditions are given for the existence of a causal stable solution for general bilinear time series with time-dependent coefficients.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2003.11.017
Bibi, Abdelouahab 1

1 Département de mathématiques, laboratoire de mathématiques appliquées et modélisation, Université Mentouri, Constantine, Algeria 
@article{CRMATH_2004__338_3_245_0,
     author = {Bibi, Abdelouahab},
     title = {On the stability and causality of general time-dependent bilinear~models},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {245--248},
     publisher = {Elsevier},
     volume = {338},
     number = {3},
     year = {2004},
     doi = {10.1016/j.crma.2003.11.017},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.crma.2003.11.017/}
}
TY  - JOUR
AU  - Bibi, Abdelouahab
TI  - On the stability and causality of general time-dependent bilinear models
JO  - Comptes Rendus. Mathématique
PY  - 2004
SP  - 245
EP  - 248
VL  - 338
IS  - 3
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/j.crma.2003.11.017/
DO  - 10.1016/j.crma.2003.11.017
LA  - en
ID  - CRMATH_2004__338_3_245_0
ER  - 
%0 Journal Article
%A Bibi, Abdelouahab
%T On the stability and causality of general time-dependent bilinear models
%J Comptes Rendus. Mathématique
%D 2004
%P 245-248
%V 338
%N 3
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/j.crma.2003.11.017/
%R 10.1016/j.crma.2003.11.017
%G en
%F CRMATH_2004__338_3_245_0
Bibi, Abdelouahab. On the stability and causality of general time-dependent bilinear models. Comptes Rendus. Mathématique, Tome 338 (2004) no. 3, pp. 245-248. doi : 10.1016/j.crma.2003.11.017. http://archive.numdam.org/articles/10.1016/j.crma.2003.11.017/

[1] Bibi, A.; Oyet, A. A note on the properties of some time-varying bilinear models, Statist. Probab. Lett., Volume 58 (2002), pp. 399-411

[2] Bibi, A. On the covariance structure of the time-varying bilinear models, Stochastic Anal. Appl., Volume 21 (2003) no. 1, pp. 25-60

[3] Dahlhaus, R. On the Kullback–Leibler information divergence of locally stationary processes, Stochastic Proc. Appl., Volume 62 (1996), pp. 139-168

[4] Guégan, D. Different representations for bilinear models, J. Time Series Anal., Volume 8 (1987) no. 4, pp. 389-408

[5] Miller, K.S. Linear Difference Equations, Benjamin, New York, 1968

[6] Subba Rao, T. The bispectral analysis of non linear stationary time series with reference to bilinear time series models (Brillinger, D.R.; Krishnaiah, P.R., eds.), Handbook of Statistics, vol. 3, 1983, pp. 293-319

[7] Subba Rao, T. Statistical analysis of nonlinear and nongaussian time series models (Csiszar, I.; Michaeltzky, G., eds.), Stochastic Differential and Difference Equations, Birkhäuser Boston, 1997, pp. 285-298

Cité par Sources :