×

zbMATH — the first resource for mathematics

Positivity of the exponent for stationary sequences of matrices. (English) Zbl 0591.60036
Lyapunov exponents, Proc. Workshop, Bremen/Ger. 1984, Lect. Notes Math. 1186, 56-73 (1986).
[For the entire collection see Zbl 0577.00017.]
A condition is given which ensures the property in the title. It is shown that this condition generalizes altogether H. Furstenberg’s criterion [Trans. Am. Math. Soc. 108, 377-428 (1963; Zbl 0203.191)], its known extensions and also S. Kotani [Stochastic analysis, Proc. Taniguchi Int. Symp., Katata & Kyoto/Jap. 1982, North-Holland Math. Libr. 32, 225-247 (1984; Zbl 0549.60058)] and B. Simon [Commun. Math. Phys. 89, 227-234 (1983; Zbl 0534.60057)] result for Jacobi matrices.

MSC:
60G10 Stationary stochastic processes
15B52 Random matrices (algebraic aspects)