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Product of Random Stochastic Matrices.
- Source :
-
IEEE Transactions on Automatic Control . Feb2014, Vol. 59 Issue 2, p437-448. 12p. - Publication Year :
- 2014
-
Abstract
- The paper deals with the convergence properties of the products of random (row-)stochastic matrices. The limiting behavior of such products is studied from a dynamical system point of view. In particular, by appropriately defining a dynamic associated with a given sequence of random (row-)stochastic matrices, we prove that the dynamics admits a class of time-varying Lyapunov functions, including a quadratic one. Then, we discuss a special class of stochastic matrices, a class \cal P^\ast, which plays a central role in this work. We then study cut-balanced chains and using some geometric properties of these chains, we characterize the stability of a subclass of cut-balanced chains. As a special consequence of this stability result, we obtain an extension of a central result in the non-negative matrix theory stating that, for any aperiodic and irreducible row-stochastic matrix A, the limit \limk\rightarrow\inftyA^{k} exists and it is a rank one stochastic matrix. We show that a generalization of this result holds not only for sequences of stochastic matrices but also for independent random sequences of such matrices. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189286
- Volume :
- 59
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Automatic Control
- Publication Type :
- Periodical
- Accession number :
- 94017073
- Full Text :
- https://doi.org/10.1109/TAC.2013.2283750