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The Berger-Wang formula establishes equality between the joint andgeneralized spectral radii of a set of matrices. For matrix products whosemultipliers are applied not arbitrarily but in accordance with some Markovianlaw, there are also known analogs of the joint and generalized spectral radii.However, the known proofs of the Berger-Wang formula hardly can be directlyapplied in the case of Markovian products of matrices since they essentiallyrely on the arbitrariness of appearance of different matrices in the relatedmatrix products. Nevertheless, as has been shown by X. Dai the Berger-Wangformula is valid for the case of Markovian analogs of the joint and thegeneralized spectral radii too, although the proof in this case heavilyexploits the more involved techniques of multiplicative ergodic theory. In thepaper we propose a matrix theory construction allowing to deduce the Markoviananalog of the Berger-Wang formula from the classical Berger-Wang formula.

The Berger-Wang formula for the Markovian joint spectral radius