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.
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.
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