Existence of moments in a stationary stochastic difference equation

The stationary stochastic difference equation Xt = YtXt.1 + Wt is analyzed with emphasis on conditions ensuring that ||Xt||p <.. Some general results are obtained and then applied to different classes of input processes {(Yt, Wt)}. Especially both necessary and sufficient conditions are given in the Gaussian case. We also obtain results concerning moments of products of dependent variables.