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Variational calculus for Gaussian random fields

  • Stochastic Finite Dimensional Systems
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Stochastic Systems and Optimization

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 136))

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References

  1. P. Lévy, Sur la variation de la distribution de l'électricité sur un conducteur dont la surface se déforme. Bull. Société math. de France, 46 (1918), 35–68.

    Google Scholar 

  2. —, Problèmes concrets d'analyse fonctionnelle. Cauthier-Villars, Paris, 1951, Part. I, II.

    Google Scholar 

  3. —, A special problem of Brownian motion, and a general theory of Gaussian random functions. Proc. 3rd Berkeley Symp. vol.II (1965), 133–175.

    Google Scholar 

  4. K. Aomoto, Formule variationelle d'Hadamard et modèle des variétés différentiables plongées. J. Functional Analysis 34 (1979), 493–523.

    Google Scholar 

  5. T. Hida, Brownian motion (in Japanese). Iwanami Pub. Co., Tokyo 1975; English Trans. Springer-Verlag, New York Heidelberg Berlin 1980.

    Google Scholar 

  6. —, Analysis of Brownian functionals. Carleton Math. Lec. Notes, no.13, Carleton Univ. Ottawa, 1975.

    Google Scholar 

  7. —, A note on generalized Gaussian random fields. Jounal Multivariate Analysis 27 (1988), 255–260.

    Google Scholar 

  8. —, White noise analysis and Gaussian random fields. Proc. 24th Winter School of Theoretical Physics, Karpacz, 1988, to appear.

    Google Scholar 

  9. T. Hida, K.-S. Lee and S.-S. Lee, Conformal invariance of white noise. Nagoya Math. J. 98 (1985), 87–98.

    Google Scholar 

  10. T. Hida, K.-S. Lee and Si Si, Multidimensional parameter white noise and Gaussian random fields. Balakrishnan volume (1987), 177–183.

    Google Scholar 

  11. H.-H. Kuo, Brownian functionals and applications, Acta Appl. Math. 1 (1983), 175–188.

    Google Scholar 

  12. K.-S. Lee, White noise approach to Gaussian random fields. to appear, 1989.

    Google Scholar 

  13. J.L. Lions and E. Magenes, Non-homogeneous boundary value problems and applications, vol. I, Springer-Verlag, New York Heidelberg Berlin, 1972.

    Google Scholar 

  14. Si Si, A note on Lévy's Brownian motion. Nagoya Math. J. 108 (1987), 121–130.

    Google Scholar 

  15. —, Gaussian processes and conditional expectations. BiBoS Notes 292/87, Univ. Bielefeld, 1987.

    Google Scholar 

  16. —, Topics on Gaussian random fields. RIMS Kokyuroku, #672 (1988), Gaussian Random Fields — Stochastic Variational Calculus and Related Topics, ed. A. Noda.

    Google Scholar 

  17. Y. Yokoi, Positive generalized white noise functionals. Preprint, Kumamoto, 1987; to appear 1989.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Nagoya University, 464-01, Nagoya, Japan

    Takeyuki Hida

  2. Department of Mathematics, Rangoon University, Rangoon, Burma

    Si Si

Authors
  1. Takeyuki Hida
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  2. Si Si
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Editor information

Jerzy Zabczyk

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© 1989 Springer-Verlag

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Hida, T., Si, S. (1989). Variational calculus for Gaussian random fields. In: Zabczyk, J. (eds) Stochastic Systems and Optimization. Lecture Notes in Control and Information Sciences, vol 136. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0002671

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  • DOI: https://doi.org/10.1007/BFb0002671

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51619-4

  • Online ISBN: 978-3-540-46719-9

  • eBook Packages: Springer Book Archive

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