no. 1
Probability Theory
Tail of the stationary solution of the stochastic equation Yn+1=anYn+bn with Markovian coefficients
[Queue de la solution stationnaire de l'équation Yn+1=anYn+bn à coefficients markoviens]
Présenté par : Marc Yor
de Saporta, Benoîte1
1 IRMAR, université de Rennes I, campus de Beaulieu, 35042 Rennes cedex, France
Comptes Rendus. Mathématique, Tome 340 (2005) no. 1, pp. 55-58

In this Note, we deal with the real stochastic difference equation Yn+1=anYn+bn, n∈Z, where the sequence (an) 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.

On étudie la queue de la solution stationnaire de l'équation Yn+1=anYn+bn, n∈Z, où (an) est une chaîne de Markov à espace d'états fini. Par des méthodes de renouvellement, on donne une caractérisation détaillée du cas où la queue est polynômiale.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2004.11.018

de Saporta, Benoîte 1

1 IRMAR, université de Rennes I, campus de Beaulieu, 35042 Rennes cedex, France 
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de Saporta, Benoîte. Tail of the stationary solution of the stochastic equation $ {Y}_{n+1}={a}_{n}{Y}_{n}+{b}_{n}$ with Markovian coefficients. Comptes Rendus. Mathématique, Tome 340 (2005) no. 1, pp. 55-58. doi: 10.1016/j.crma.2004.11.018

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