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Error Bounds for Nonnegative Dynamic Models

Author

Listed:
  • N. M. Van Dijk

    (University of Amsterdam)

  • K. Sladký

    (Academy of Sciences of the Czech Republic)

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.

Suggested Citation

  • N. M. Van Dijk & K. Sladký, 1999. "Error Bounds for Nonnegative Dynamic Models," Journal of Optimization Theory and Applications, Springer, vol. 101(2), pages 449-474, May.
    • Handle: RePEc:spr:joptap:v:101:y:1999:i:2:d:10.1023_a:1021749829267
    DOI: 10.1023/A:1021749829267
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    References listed on IDEAS

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    1. Ward Whitt, 1978. "Approximations of Dynamic Programs, I," Mathematics of Operations Research, INFORMS, vol. 3(3), pages 231-243, August.
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