TY - JOUR

T1 - Erratum

T2 - Nonconventional random matrix products (Electronic Communications in Probability, (2018) 23, 10.1214/18-ECP140)

AU - Kifer, Yuri

AU - Sodin, Sasha

N1 - Publisher Copyright:
© 2019, Institute of Mathematical Statistics. All rights reserved.

PY - 2019

Y1 - 2019

N2 - The proof of Theorem 2.3 in our paper [3] is fully justified only under the additional assumption qi(n) = ain + bi, i = 1, …, ℓ. Correction in Markov case In the statement of Theorem 2.3, an additional assumption qi(n) = ain + bi 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 ξn, n ≥ 0. Without this assumption, Ξn, 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.

AB - The proof of Theorem 2.3 in our paper [3] is fully justified only under the additional assumption qi(n) = ain + bi, i = 1, …, ℓ. Correction in Markov case In the statement of Theorem 2.3, an additional assumption qi(n) = ain + bi 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 ξn, n ≥ 0. Without this assumption, Ξn, 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.

UR - http://www.scopus.com/inward/record.url?scp=85066498324&partnerID=8YFLogxK

U2 - 10.1214/19-ECP210

DO - 10.1214/19-ECP210

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AN - SCOPUS:85066498324

SN - 1083-589X

VL - 24

JO - Electronic Communications in Probability

JF - Electronic Communications in Probability

M1 - 6

ER -