Tuğrul Dayar, Jean-Michel Fourneau, Nihal Pekergin (2010)
RAIRO - Operations Research
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We present a transformation for stochastic matrices and analyze the effects of using it in stochastic comparison with the strong stochastic (st) order. We show that unless the given stochastic matrix is row diagonally dominant, the transformed matrix provides better st bounds on the steady state probability distribution.
Kojecký, Tomáš, Mayer, Petr
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We provide a short overview of algorithms useful for computing of stationary probability vectors of stochastic matrix. Some care is devoted to the problem of computing of all extremal stationary probability vectors for the reducible stochastic matrices. We present some modifications of standard Iterative Aggregation/Disaggregation algorithm.
Ivo Marek, Petr Mayer (2002)
Applications of Mathematics
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The paper surveys some recent results on iterative aggregation/disaggregation methods (IAD) for computing stationary probability vectors of stochastic matrices and solutions of Leontev linear systems. A particular attention is paid to fast IAD methods.
George Hutchinson (2016)
Special Matrices
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We disprove a conjecture made by Rajesh Pereira and Joanna Boneng regarding the upper bound on the number of doubly quasi-stochastic scalings of an n × n positive definite matrix. In doing so, we arrive at the true upper bound for 3 × 3 real matrices, and demonstrate that there is no such bound when n ≥ 4.
Lakshmi Kanta Patra, Suchandan Kayal, Phalguni Nanda (2018)
Applications of Mathematics
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We focus on stochastic comparisons of lifetimes of series and parallel systems consisting of independent and heterogeneous new Pareto type components. Sufficient conditions involving majorization type partial orders are provided to obtain stochastic comparisons in terms of various magnitude and dispersive orderings which include usual stochastic order, hazard rate order, dispersive order and right spread order. The usual stochastic order of lifetimes of series systems with possibly different...