Abstract :
Consider the nonhomogeneous linear recurrence system
xn+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.
