SIAM Journal on Control and Optimization · 1988 · 54 citations · 23 references
Natural SciencesMathematicsDynamical SystemsProbability TheoryStochastic ProcessesControl TheoryDiffusion ProcessesErgodic TheoryMarkov ProcessesOptimal ControlStochastic ControlDiffusionsErgodic ProcessesErgodicity ConditionsErgodicity Of DiffusionsMarkov Diffusion ProcessesMultidimensional DiffusionsOptimal Control Of Stochastic SystemsStochastic Optimal Control
The existence of optimal stable Markov relaxed controls for the ergodic control of multidimensional diffusions is established by direct probabilistic methods based on a characterization of a.s. limit sets of empirical measures. The optimality of the above is established in the strong (i.e., almost sure) sense among all admissible controls under very general conditions.
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Markov Processes: Characterization and Convergence.
Andris Abakuks, S. N. Ethier, Thomas G. Kurtz · Biometrics · 1987 · 4.5K citations