Dominant and Recessive Solutions of Symmetric Three Term Recurrences

Dominant and recessive solutions are defined for matrix three term recurrences −KnXn+1 + BnXn − KTn−1Xn−1 =0.Eventual disconjugacy is shown to imply existence of a recessive solution at ∞ and, furthermore, that an associated Riccati equation Wn+1 = An + E−1nWn(Wn + Cn−1)−1Cn−1(ETn)−1has an eventually minimal solution W−n. Riccati equations of this form with An and Cn positive definite arise in the discrete regulator problem.