Tail of the stationary solution of the stochastic equation [formula omitted] with Markovian coefficients

Abstract

In this Note, we deal with the real stochastic difference equation Y n + 1 = a n Y n + b n , n ∈ Z , where the sequence ( a n ) 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).