In this paper we consider the multivariate equation Xₙ₊₁ = Aₙ₊₁Xₙ + Bₙ₊₁ with i.i.d. coefficients which have only a logarithmic moment. We give a necessary and sufficient condition for existence of a strictly stationary solution independent of the future. As an application we characterize the multivariate ARMA equations with general noise which have such a solution.
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Bougerol et al. (1992) studied this question.