Abstract
A family of subalgebras describing the space of complex-valued 2×2 matrices is selected. In this space, a stochastic semigroupY n =X n X −1 ...X 1,n= \(\overline {1, \infty } \), is considered, where {Xi, i=\(\overline {1, \infty } \)} are independent equally distributed random matrices taking two values. For a stochastic semigroupY n , whose phase space belongs to one of the subalgebras, the index of exponential growth is determined explicitly.
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References
H. Furstenberg and H. Kesten, “Products of random matrices,”Ann. Math. Statist.,31, 457–469 (1960).
A. S. Chani, “Asymptotic behavior of products of some classes of random matrices in the Bernoulli scheme,”Random Oper. Stock. Eqs.,1, No. 3, 19–24 (1992).
M. Marcus and H. Mine,A Survey of Matrix Theory and Matrix Inequalities [Russian translation], Nauka, Moscow (1972).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 11, pp. 1580–1584, November, 1993.
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Chani, A.S. Asymptotic behavior of a class of stochastic semigroups in the Bernoulli scheme. Ukr Math J 45, 1779–1784 (1993). https://doi.org/10.1007/BF01060866
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DOI: https://doi.org/10.1007/BF01060866