On the continuous singularity of the limit distribution of products of i. i. d. \(d\times d\) stochastic matrices
In generalizing earlier results [cp. e.g. \textit{T.-C. Sun}, Bull. Inst. Math., Acad. Sin. 3, 235-248 (1975; Zbl 0327.60009); \textit{A. Nakassis}, J. Math. Anal. Appl. 70, 337-347 (1979; Zbl 0426.60012); and the authors and \textit{J. S. Ratti}, J. Theor. Probab. 12, No.~2, 571-583 (1999; Zbl 0943.60010) and ibid. 12, No.~4, 1109-1112 (1999; Zbl 0961.60014)] the authors give sufficient conditions for the limit distribution of products of i.i.d. \(d\times d\) random stochastic matrices, \(d\) finite and \(d\geq 2\), to be continuous singular, when the support of the distribution of the individual random matrices is finite or countably infinite. The proofs are based on applications of the multivariate central limit theorem. The references contain ten bibliographical hints.
product of independent identically distributed stochastic matrices
scientific article; zbMATH DE number 1892251