A fluctuation theory for Markov chains |
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| Authors: | V.G. Kulkarni N.U. Prabhu |
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| Affiliation: | Curriculum in Operations Research and Systems Analysis, University of North Carolina, Chapel Hill, NC 27514, USA;School of Operations Research and Industrial Engineering Cornell University, Ithaca, NY 14853, USA |
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| Abstract: | A fluctuation theory for Markov chains on an ordered countable state space is developed, using ladder processes. These are shown to be Markov renewal processes. Results are given for the joint distribution of the extremum (maximum or minimum) and the first time the extremum is achieved. Also a new classification of the states of a Markov chain is suggested. Two examples are given. |
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| Keywords: | Markov chains maximum and minimum functionals ladder processes Wiener-Hopf factorization |
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