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Applied Mathematics and Optimization

, Volume 41, Issue 1, pp 1–7 | Cite as

A Simple Proof of the Theorem Concerning Optimality in a One-Dimensional Ergodic Control Problem

  • Y. Fujita
  • 47 Downloads

Abstract.

We give a simple proof of the theorem concerning optimality in a one-dimensional ergodic control problem. We characterize the optimal control in the class of all Markov controls. Our proof is probabilistic and does not need to solve the corresponding Bellman equation. This simplifies the proof.

Key words. Ergodic control, Markov controls, {Č}eby{š}ev's inequality. AMS Classification. 93E20, 93C40. 

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Copyright information

© Springer-Verlag New York Inc. 2000

Authors and Affiliations

  • Y. Fujita
    • 1
  1. 1.Department of Mathematics, Faculty of Science, Toyama University, Toyama 930-8555, Japan JP

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