The stochastic equation Yn +1=AnYn + Bn with stationary coefficients

Abstract

In this note we deal with the stochastic difference equation of the form Y n+1 = AnYn + Bn , n∊ℤ, where the sequence is assumed to be strictly stationary and ergodic. By means of simple arguments a unique stationary solution of this equation is constructed. The stability of the stationary solution is the second subject of investigation. It is shown that under some additional assumptions