Livšic regularity for random and sequential dynamics through transfer operators

The paper proves the random Livšic regularity theorem via twisted transfer-operator perturbation theory and a martingale-coboundary decomposition, yielding the closed-form expression (23) and B-regularity of H; the model gives a direct backward-iteration/transfer-operator proof that also produces (23). The model’s only delicate point is its Neumann-series argument for 1/v_ω ∈ B_ω; while likely valid under the paper’s (V1)-(V9) framework, it needs a short justification (or can be bypassed exactly as the paper does by normalizing the transfer operators).