Ergodic Control of Partially Degenerate Diffusions in a Compact Domain

Abstract

The problem of ergodic control of a reflecting diffusion in a compact domain is analysed under the condition of partial degeneracy, i.e. when its transition kernel after some time is absolutely continuous with respect to the Lebesgue measure on a part of the state space. Existence of a value function and a “martingale dynamic programming principle” are established by mapping the problem to a discrete time control problem. Implications for existence of optimal controls are derived.

Keywords:

• Controlled diffusion
• Ergodic control
• Dynamic programming principle
• Optimal controls
• 93E20

Acknowledgements

The authors thank an anonymous referee for pointing out errors in an earlier version.

Notes

Research partially supported by Grant No. DST/MS/III-045/96 from the Department of Science and Technology, Government of India.

^‡E-mail: [email protected]