Multiple time scale decomposition of discrete time Markov chains |
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Authors: | J R Rohlicek |
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Affiliation: | 1. School of Ecology and Nature Conservation, Beijing Forestry University, Beijing, 100083, PR China;2. The Key Laboratory of Ecological Protection in the Yellow River Basin of National Forestry and Grassland Administration, Beijing, 100083, PR China;1. German Aerospace Center (DLR), German Remote Sensing Data Center (DFD), Land Surface Applications, Oberpfaffenhofen, D-82234 Weßling, Germany;2. Karlsruhe Institute of Technology (KIT), Institute of Photogrammetry and Remote Sensing (IPF), Englerstr. 7, D-76131 Karlsruhe, Germany |
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Abstract: | The multiple time scale decomposition of discrete time, finite state Markov chains is addressed. In 1, 2], the behavior of a continuous time Markov chain is approximated using a fast time scale, ε-independent, continuous time process, and a reduced order perturbed process. The procedure can then be iterated to obtain a complete multiple time scale decomposition. In the discrete time case presented in this paper, the basic approximation has a ‘hybrid’ form. In this form, the fast time scale behavior is approximated using an ε-independent, discrete time Markov chain, and the slow behavior is captured by a perturbed, continuous time process. Further time scale decomposition then involves the continuous time procedure in 1, 2]. This extension to discrete time chains bridges previous multiple time scale decomposition results, which have dealt exclusively with either continuous time or discrete time processes, and provides a uniform framework for the analysis of both types of systems. |
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Keywords: | Markov process Discrete time Aggregation Perturbation theory Multiple time scales |
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