Monotone matrices and monotone Markov processes |
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Authors: | Julian Keilson Adri Kester |
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Affiliation: | The University of Rochester, Rochester, N.Y., 14627, U.S.A. |
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Abstract: | A stochastic matrix is “monotone” [4] if its row-vectors are stochastically increasing. Closure properties, characterizations and the availability of a second maximal eigenvalue are developed. Such monotonicity is present in a variety of processes in discrete and continous time. In particular, birth-death processes are monotone. Conditions for the sequential monotonicity of a process are given and related inequalities presented. |
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Keywords: | monotone Markov chains domination continuous time chains time-reversibility birth-death processes |
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