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Comptes Rendus Mathématique
Volume 340, n° 1
pages 55-58 (janvier 2005)
Doi : 10.1016/j.crma.2004.11.018
Received : 8 January 2004 ;  accepted : 3 November 2004
Tail of the stationary solution of the stochastic equation   with Markovian coefficients
Queue de la solution stationnaire de lʼéquation   à coefficients markoviens
 

Benoîte de Saporta
IRMAR, université de Rennes I, campus de Beaulieu, 35042 Rennes cedex, France 

Abstract

In this Note, we deal with the real stochastic difference equation  ,  , where the sequence   is a finite state space Markov chain. By means of the renewal theory, we give a precise description of the situation where the tail of its stationary solution exhibits power law behavior. To cite this article: B. de Saporta, C. R. Acad. Sci. Paris, Ser. I 340 (2005).

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Résumé

On étudie la queue de la solution stationnaire de lʼéquation  ,  , où   est une chaîne de Markov à espace dʼétats fini. Par des méthodes de renouvellement, on donne une caractérisation détaillée du cas où la queue est polynômiale. Pour citer cet article : B. de Saporta, C. R. Acad. Sci. Paris, Ser. I 340 (2005).

The full text of this article is available in PDF format.


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