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On the limiting set of stochastic products $ xA\sb{1}\cdots A\sb{k}$


Author: D. J. Hartfiel
Journal: Proc. Amer. Math. Soc. 81 (1981), 201-206
MSC: Primary 15A51
DOI: https://doi.org/10.1090/S0002-9939-1981-0593457-5
MathSciNet review: 593457
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Abstract: In this paper we study the sequential limiting set $ L$ of the sequence $ {R_1}, \ldots ,{R_k} = \{ x{A_1} \ldots {A_k}\vert x$ is a stochastic vector, and $ {A_i}$ a stochastic matrix with $ P \leqslant {A_i} \leqslant Q$, for nonnegative matrices $ P$ and $ Q\} , \ldots $. We characterize $ L$ and provide some work on approximating $ L$.


References [Enhancements On Off] (What's this?)

  • [1] Adi Ben-Israel, Generalized inverses: theory and applications, Wiley, New York, 1974. MR 0396607 (53:469)
  • [2] F. R. Gantmacher, The theory of matrices, Vol. 2, Chelsea, New York, 1964.
  • [3] D. J. Hartfiel, On infinite products of nonnegative matrices, SIAM J. Appl. Math. 26 (1974), 297-301. MR 0352144 (50:4631)
  • [4] Marvin Marcus and Henryk Minc, A survey of matrix theory and matrix inequalities, Allyn and Bacon, Boston, Mass., 1964. MR 0162808 (29:112)
  • [5] R. L. Moore, Foundations of point set theory, Amer. Math. Soc. Colloq. Publ., vol. 13, Amer. Math. Soc., Providence, R.I., 1962. MR 0150722 (27:709)
  • [6] T. C. Wesselkamper, A Markov model of cyclic structured programs (preprint).

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DOI: https://doi.org/10.1090/S0002-9939-1981-0593457-5
Article copyright: © Copyright 1981 American Mathematical Society

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