Abstract
A family of infinite time horizon, discounted cost and ergodic cost control problems are formulated and explicitly solved in noncompact symmetric spaces that are symmetric tubes or Siegel domains. Similar results can be verified for symmetric cones so that all classical symmetric spaces can be included as well as four exceptional symmetric spaces. For each spherical polynomial, a solvable control problem on each of these symmetric spaces is given. The problems are to control a Brownian motion in the symmetric space by a drift vector field so that the resulting process remains close to the origin. The control problem has an invariance under the maximal compact subgroup K for the symmetric space that is inherited from the K-invariance of the spherical polynomials.
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Duncan, T.E. (1999). Solvable Infinite Time Horizon Stochastic Control Problems in Noncompact Symmetric Spaces. In: McEneaney, W.M., Yin, G.G., Zhang, Q. (eds) Stochastic Analysis, Control, Optimization and Applications. Systems & Control: Foundations & Applications. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1784-8_22
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DOI: https://doi.org/10.1007/978-1-4612-1784-8_22
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