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Gaussian processes: Nonlinear analysis and stochastic calculus

Homogeneous Chaos And Multiple Wiener Integrals

Part of the Lecture Notes in Mathematics book series (LNM,volume 695)

Keywords

  • Tensor Product
  • Gaussian Process
  • Stochastic Differential Equation
  • Sample Path
  • Wiener Process

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References

  1. Fréchet, M. (1910). Sur les fonctionnelles continues. Ann. Éc. Norm. 27, 193–216.

    MathSciNet  MATH  Google Scholar 

  2. Friedman, A. (1976). Stochastic Differential Equations, Vol. 1,2. Academic Press, New York.

    MATH  Google Scholar 

  3. Huang, S.T. and Cambanis, S. (1976). Stochastic and multiple Wiener integrals for Gaussian processes. Institute of Statistics Mimeo Series No. 1087, University of North Carolina at Chapel Hill. To appear in Ann. Probability.

    Google Scholar 

  4. Huang, S.T. and Cambanis, S. (1976). On the representation of nonlinear systems with Gaussian inputs. Proc. Fourteenth Allerton Conference on Circuit and System Theory, 451–459.

    Google Scholar 

  5. Huang, S.T. (1977). Stochastic integrals for Gaussian processes: The differential formula. Manuscript under preparation.

    Google Scholar 

  6. Kakutani, S. (1961). Spectral analysis of stationary Gaussian processes. Proc. Fourth Berkeley Symp. Math. Statist. Probability, Vol. 2, 239–247. Univ. of California Press, Berkeley.

    Google Scholar 

  7. Kallianpur, G. (1970). The role of reproducing kernel Hilbert spaces in the study of Gaussian processes. In Ney, P. (Ed.), Advances in Probability and Related Topics, Vol. 2, 49–83, Marcel Dekker, New York.

    Google Scholar 

  8. Kunita, H. and Watanabe, S. (1967). On square integrable martingales. Nagoya Math. J. 30, 209–245.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. McKean, H.P. (1973). Wiener's theory of nonlinear noise. In Stochastic Differential Equations, SIAM-AMS Proc. Vol. VI, 191–209.

    MathSciNet  MATH  Google Scholar 

  10. Meyer, P.A. (1976). Un cours sur les intégrales stochastiques. In Séminaire de Probabilités X. Lecture Notes in Math. no. 511. Springer, Berlin.

    Google Scholar 

  11. Neveu, I. (1968). Processus Aléatoires Gaussiens. Les Presses de l'Université de Montréal.

    Google Scholar 

  12. Skorokhod, A.V. (1975). On a generalization of a stochastic integral. Theor. Probability Appl. 20, 219–233.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. Wiener, N. (1958). Nonlinear Problems in Random Theory. Wiley, New York.

    MATH  Google Scholar 

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© 1978 Springer-Verlag

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Huang, S.T., Cambanis, S. (1978). Gaussian processes: Nonlinear analysis and stochastic calculus. In: Kallianpur, G., Kölzow, D. (eds) Measure Theory Applications to Stochastic Analysis. Lecture Notes in Mathematics, vol 695. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062664

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  • DOI: https://doi.org/10.1007/BFb0062664

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09098-4

  • Online ISBN: 978-3-540-35556-4

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