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Compact representation of the Hadamard function in a multidimensional space, based on the integral correlation matrix operator

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Abstract

For the multicomponent Ornstein-Uhlenbeck stochastic process, we derive a compact representation of the generating function of the integral quadratic performance functional. This representation may be used to solve the control problem for a distributed stochastic process.

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References

  1. Yu. M. Astapov and V. S. Medvedev, Statistical Theory of Automatic Regulation and Control Systems [in Russian], Moscow (1982).

  2. A. G. Butkovskii and L. M. Pustyl'nikov, Theory of Moving Control of Distributed-Parameter Systems [in Russian], Moscow (1980).

  3. H.-S. Ho, Gaussian Measures in Banach Spaces [Russian translation], Moscow (1979).

  4. B. R. Levin, Theoretical Principles of Statistical Radio Engineering [in Russian], Moscow (1969).

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Translated from Vychislitel'naya i Prikladnaya Matematika, No. 66, pp. 104–106, 1988.

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Kostenko, Y.T., Mazmanishvili, A.S. Compact representation of the Hadamard function in a multidimensional space, based on the integral correlation matrix operator. J Math Sci 66, 2435–2437 (1993). https://doi.org/10.1007/BF01364979

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  • DOI: https://doi.org/10.1007/BF01364979

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