The development of information-growth laws reveals mutual-information rates under specific conditions, enhancing understanding of linear systems.
We develop information-growth laws for partially observed random linear cocycles. Under exterior faithfulness conditions, the ordered eigenvalues of the cumulative Fisher information recover the positive observable Lyapunov spectrum, yielding exact mutual-information and posterior-contraction rates. We also treat dark quotients, non-Gaussian absolutely continuous priors, polynomial growth at zero exponents, intermittent sensing, and Blackwell comparison.
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Hiroyuki Shioiri (2026) studied this question.
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