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System stability and optimal control

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Abstract

Stochastic models arising in inventory, insurance, queueing theory, and other areas are considered. The underlying process is a random walk with two absorbing boundaries, 0 and n. It is proved that the introduction of a multi-level control radically changes the asymptotic behavior (as n→∞) of normalized absorption time and simultaneously stabilizes the system. Some optimization problems are solved as well.

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Authors and Affiliations

  1. Moscow State University, Vorob'yovy Gory, 119899, Moscow, Russia

    E. V. Bulinskaya

Authors
  1. E. V. Bulinskaya
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Additional information

Supported by the Russian Foundation for Fundamental Research (grant No. 96-01-01092).

Proceedings of the Seminar on Stability Problems for Stochastic Models, Hajdúszoboszló, Hungary, 1997, Part I.

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Bulinskaya, E.V. System stability and optimal control. J Math Sci 92, 3857–3872 (1998). https://doi.org/10.1007/BF02432356

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  • DOI: https://doi.org/10.1007/BF02432356

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