Optimal ergodic control of Markov diffusion processes with minimum variance

Abstract

In this paper, we study the optimal ergodic control problem with minimum variance for a general class of controlled Markov diffusion processes. To this end, we follow a lexicographical approach. Namely, we first identify the class of average optimal control policies, and then within this class, we search policies that minimize the limiting average variance. To do this, a key intermediate step is to show that the limiting average variance is a constant independent of the initial state. Our proof of this latter fact gives a result stronger than the central limit theorem for diffusions. An application to manufacturing systems illustrates our results.

Keywords:

• controlled diffusions
• ergodic control
• variance minimization

2000 Mathematics Subject Classification::

• 93E20
• 60J60

Acknowledgements

We wish to thank Prof. Tomas Prieto-Rumeau for bringing to our attention the method of moments mentioned in Remark 3.1. This research was partially supported by CONACyT grant 104001.

Notes

^1. [email protected].

Additional information

Notes on contributors

Onésimo Hernández-Lerma

1 1. [email protected].