Erratum: Nonconventional random matrix products (Electronic Communications in Probability, (2018) 23, 10.1214/18-ECP140)

The proof of Theorem 2.3 in our paper [3] is fully justified only under the additional assumption q_i(n) = a_in + b_i, i = 1, …, ℓ. Correction in Markov case In the statement of Theorem 2.3, an additional assumption q_i(n) = a_in + b_i is required which yields a homogeneous in time ℓ-component Markov chain (Formula Presented) with transition probabilities (Formula Presented) where (Formula Presented) is the k-step transition probability of the initial Markov chain ξ_n, n ≥ 0. Without this assumption, Ξ_n, n ≥ 0 forms, in general, an inhomogeneous Markov chain (even when ℓ = 1), and so the limits (Lyapunov exponents) in (2.8) may fail to exists. In addition, the large deviations estimates and other results from [1] and [2] we relied upon are proved there for homogeneous Markov chains only.