(a) Assume that the top Lyapunov coefficient γ of the sequence {At, t ∈ Z}, defined in (4.70), is strictly negative. Show the spectral radius of the sequence {At, t ∈ Z} is larger than the spectral radius of the deterministic obtained by zeroing the coefficients of the first p rows and of the first p columns of the matrix At.
b) Show that this matrix has the same nonzero eigenvalues as B (defined in (4.96)), and thus the same spectral radius. Deduce that γ <>
(c) Show that the three following conditions are equivalent:
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