Asymptotic Behavior of a Nonhomogeneous Linear Recurrence System

AbstractConsider the nonhomogeneous linear recurrence systemxn+1=(A+Bn)xn+gn,where A and Bn (n=0,1,…) are square matrices and gn (n=0,1,…) are column vectors. In this paper, we describe, in terms of the initial condition, the asymptotic behavior of the solutions of this equation in the case when A has a simple dominant eigenvalue λ0,∑n=0∞⫫Bn⫫<∞ and ∑n=0∞|λ0|−n⫫gn⫫<∞. The proof is based on the duality between the solutions of the above equation and the solutions of the associated adjoint equation. As a consequence, we obtain a similar result for higher order scalar equations