Comptes Rendus
Probability Theory
On the multidimensional stochastic equation Yn+1=AnYn+Bn
Comptes Rendus. Mathématique, Volume 339 (2004) no. 7, pp. 499-502.

We study the behavior at infinity of the tail of the stationary solution of a multidimensional linear auto-regressive process with random coefficients. We exhibit an extended class of multiplicative coefficients satisfying a condition of irreducibility and proximality that yield to a heavy tail behavior.

On étudie le comportement à l'infini de la queue de la solution stationnaire d'un processus auto-régressif linéaire multidimensionnel à coefficients aléatoires. On donne une vaste classe de coefficients multiplicatifs vérifiant une condition d'irréductibilité et de proximalité qui conduisent à un comportement de type queue polynomiale.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2004.07.024

Benoîte de Saporta 1; Yves Guivarc'h 1; Emile Le Page 2

1 IRMAR, université de Rennes I, campus de Beaulieu, 35042 Rennes cedex, France
2 LMAM, université de Bretagne Sud, centre Yves Coppens, campus de Tohannic, BP 573, 56017 Vannes, France
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Benoîte de Saporta; Yves Guivarc'h; Emile Le Page. On the multidimensional stochastic equation $ {Y}_{n+1}={A}_{n}{Y}_{n}+{B}_{n}$. Comptes Rendus. Mathématique, Volume 339 (2004) no. 7, pp. 499-502. doi : 10.1016/j.crma.2004.07.024. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.07.024/

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