Geodesic
On the structure of invariant measures related to noncommutative random products
Sbornik. Mathematics, Tome 20 (1973) no. 1, pp. 95-117 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $G=SL(R,n)$ be the group of mappings of the real projective space $P^{n-1}$ onto itself. There is introduced the notion of a boundary measure $\nu$ on $P^{n-1}$ for a probability measure $\mu$ on $G$, and its relation to the unique invariant measure on $P^{n-1}$ with respect to the operator $\pi(x,A)=\mu\{g\in G:gx\in A\}$ is found. It is established that the Markov chain generated by the transition probability $\pi(x,A)$ and the invariant boundary measure $\nu$ is a factor-automorphism of an automorphism of a certain Bernoulli space. A limit theorem for random mappings of a segment of the line into itself is proved. Bibliography: 6 titles. 
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E. G. Litinskii. On the structure of invariant measures related to noncommutative random products. Sbornik. Mathematics, Tome 20 (1973) no. 1, pp. 95-117. http://geodesic.mathdoc.fr/item/SM_1973_20_1_a5/

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[3] J. G. Sinai, “Mesures invariants des $Y$-systèmes”, Actes, Congrès intern. Math., t. 2, 1970, 929–940 | MR

[4] E. B. Dynkin, Markovskie protsessy, Fizmatgiz, Moskva, 1963 | MR

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[6] L. E. Dubins, D. A. Freedman, “Invariant probabilities for certain Markov processes”, Ann. Math. Stat., 37:4 (1966), 837–848 | DOI | MR | Zbl