This theoretical exploration constructs quotients to analyze zero dynamics in random systems, indicating new insights in stochastic processes.
We construct relative observable quotients for upper-triangular random linear cocycles, separating interface zero dynamics from transmitted Lyapunov directions. The theory includes exact quotient sequences, output-history realizations, cancellation classes, finite-window ranks, and Gaussian information formulas.
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Hiroyuki Shioiri (2026) studied this question.
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