On the inverse mean first passage matrix problem and the inverse M-matrix problem |
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Authors: | Michael Neumann Nung-Sing Sze |
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Institution: | a Department of Mathematics, University of Connecticut, Storrs, CT 06269-3009, United States b Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong |
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Abstract: | The inverse mean first passage time problem is given a positive matrix M∈Rn,n, then when does there exist an n-state discrete-time homogeneous ergodic Markov chain C, whose mean first passage matrix is M? The inverse M-matrix problem is given a nonnegative matrix A, then when is A an inverse of an M-matrix. The main thrust of this paper is to show that the existence of a solution to one of the problems can be characterized by the existence of a solution to the other. In so doing we extend earlier results of Tetali and Fiedler. |
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Keywords: | 60J10 60J20 15A51 15A48 |
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