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Iterative Aggregation/Disaggregation Methods for Computation Stationary Probability Vectors of Markov Chains
by
Ivo Marek
Charles University, Department of Computational Mathematics, 186 75 Praha 8, Czech Republic
A convergence theory for a general class of iterative aggregation/disaggregation (shortly IAD) methods is presented. Main results include
1. The convergence takes place for every transition matrix and covers also the case of appearance of the rare events (i.e. events possessing small probabilites) implying the bad conditioning of the corresponding transition matrices of the Markov chains under consideration.
2. Some classes of Markov chains are identified for which the examined IAD methods return the exact solutions after a finite number of iteration sweaps.
3. A particular version of the IAD methods is proposed that provides stationary probability vectors of p-cyclic Markov chains very effectively though the convergence proof does not require the frequently used assumptions that the spectrum \sigma(Bp) is real and the transition matrix B itself is consistently ordered.
4. A series of computer tests documenting the theoretical conclusions is presented.
Date received: March 21, 2001
Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. Document # cagm-29.