On Stochastic Ergodic Control in Infinite Dimensions
Some recent results on stochastic ergodic control problems in infinite- dimensional state spaces are reviewed, a special attention being paid to the ergodic control of stochastic semilinear reaction-diffusion equations. Earlier achievements obtained in this field (as well as some of those obtained for the discounted cost optimization problem) are summarized. Some of the recently obtained results that will appear in the forthcoming paper  are described in more detail.
KeywordsStochastic ergodic control Hamilton-Jacobi equation stochastic semilinear equation
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