Articlegreen1988

Ergodic Control of Multidimensional Diffusions I: The Existence Results

52 citations0/0 files storedSIAM Journal on Control and Optimization

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Stochastic processes and financial applications Stochastic processes and statistical mechanics Adaptive Dynamic Programming Control

Abstract

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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References

1983Stochastic Differential Equations and Diffusion Processes 1980MULTI-DIMENSIONAL DIFFUSION PROCESSES 1974A TRANSFORMATION OF THE PHASE SPACE OF A DIFFUSION PROCESS THAT REMOVES THE DRIFT 1981ON STRONG SOLUTIONS AND EXPLICIT FORMULAS FOR SOLUTIONS OF STOCHASTIC INTEGRAL EQUATIONS 1982Stochastic Control by Functional Analysis Methods 1970Existence of Optimal Strategies Based on Specified Information, for a Class of Stochastic Decision Problems 1978Optimality Conditions for the Average Cost per Unit Time Problem with a Diffusion Model 1983Long-term average cost control problems for continuous time Markov processes: A survey

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1990Controlled diffusions with constraints 1992Singular ergodic control for multidimensional Gaussian processes 1993Limit theorems for pathwise average cost per unit time problems for controlled queues in heavy traffic

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