Error Bounds for Nonnegative Dynamic Models

N. M. Van Dijk and K. Sladký
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N. M. Van Dijk: University of Amsterdam
K. Sladký: Academy of Sciences of the Czech Republic

Journal of Optimization Theory and Applications, 1999, vol. 101, issue 2, No 10, 449-474

Abstract: Abstract The extension of Markov reward models to dynamic models with nonnegative matrices is motivated by practical applications, such as economic input–output, employment, or population models. This paper studies the generalization of error bound theorems for Markov reward structures to dynamic reward structures with arbitrary nonnegative matrices. Both irreducible and reducible matrices are covered. In addition, results for the stochastic case are unified and extended. First, generalized expressions are derived for average reward functions. The special normalization case is distinguished and is shown to be transformable into the stochastic case. Its interpretation is of interest in itself. Next, error bound results are studied. Under a general normalization condition, it is shown that the results for the stochastic case can be extended. Both the average case and the transient case are included. A random walk-type example is included to illustrate the results.

Keywords: Markov chains; nonnegative matrices; average rewards; error bounds; bias terms; normalized cases; input–output models (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (2)

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DOI: 10.1023/A:1021749829267

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