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Stochastic Linear Controlled Systems with Quadratic Cost Revisited

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Stochastics in Finite and Infinite Dimensions

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Abstract

The subject of this article is quite classical. Indeed, the study of optimal control for continuous time diffusion processes began in the early 1960s with the stochastic linear regulator problem. We refer the reader to [1], [2], [3], [4], [8], and [9] for the literature and historical remarks related to the subject.

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References

  1. M. H. A. DavisLinear Estimation and Stochastic ControlChapman and Hall, 1977.

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  6. N. V. Krylov, Some general results in control theory, pp. 129–138 inProbab. Theory and Math. Statist. Vol. II (Vilnius, 1985), VNU Sci. Press, Utrecht1987.

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  7. P. A. MeyerProbability and Potentials’Blaisdell Publishing Company, A Division of Ginn and Company, Waltham, Massachusetts, Toronto, London, 1966.

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Krylov, N.V. (2001). Stochastic Linear Controlled Systems with Quadratic Cost Revisited. In: Hida, T., Karandikar, R.L., Kunita, H., Rajput, B.S., Watanabe, S., Xiong, J. (eds) Stochastics in Finite and Infinite Dimensions. Trends in Mathematics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0167-0_12

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  • DOI: https://doi.org/10.1007/978-1-4612-0167-0_12

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6643-3

  • Online ISBN: 978-1-4612-0167-0

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