Tail of the stationary solution of the stochastic equation with Markovian coefficients

In this paper, 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.