A trajectory-level derivation shows mutual linearity holds for non-stationary Markov jump processes and generalizes to other systems.
Meyer, A decomposition theorem for supermartin- gales, Illinois Journal of Mathematics6, 193 (1962)
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Mutual Linearity in and out of Stationarity for Markov Jump Processes: A Trajectory-Based Approach
A trajectory-level derivation shows mutual linearity holds for non-stationary Markov jump processes and generalizes to other systems.