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Notes on the Wiener semigroup and renormalization

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Séminaire de Probabilités XXV

Part of the book series: Lecture Notes in Mathematics ((SEMPROBAB,volume 1485))

Abstract

In this paper, by using white noise analysis (e.g. Wick product, scaling trasformation) we obtain some results about the ∞-dim. Wiener semigroup. A precise definition of renormalization in white noise analysis is also proposed. The main results are Theorems 2.2, 2.4, 2.5, and 3.2.

Work supported by the National Natural Science Foundation of China

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References

  1. I. Kubo and Y. Yokoi: A Remark on the testing random variables in the white noise calculus, Nagoya Math. J. Vol 115 (1989), 139–149.

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  3. H.H. Kuo, J. Potthoff and J.A. Yan: Continuity of affine transformations of white noise test functionals and application, Preprint (1990).

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  5. P.A. Meyer and J.A. Yan: Distributions sur l’espace de Wiener (suite), Sém. de Probab. XXIII, LN in Math. 1372, Springer, 1989.

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  6. J. Potthoff and J.A. Yan: Some results about test and generalized functionals of white noise, BiBoS Preprint (1989), to appear in: Proc. Singapore Probab. Conf. (1989), L.H.Y. Chen (ed.)

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  7. J.A. Yan: Products and transforms of white noise functionals, Preprint (1990).

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  8. J.A. Yan: An elementary proof of a theorem of Lee, Preprint (1990).

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Authors and Affiliations

  1. Institute of Applied Mathematics, Academia Sinica, P.O. Box 2734, 100080, Beijing, China

    J. A. Yan

Authors
  1. J. A. Yan
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Jaques Azéma Marc Yor Paul André Meyer

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© 1991 Springer-Verlag

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Yan, J.A. (1991). Notes on the Wiener semigroup and renormalization. In: Azéma, J., Yor, M., Meyer, P.A. (eds) Séminaire de Probabilités XXV. Lecture Notes in Mathematics, vol 1485. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0100848

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  • DOI: https://doi.org/10.1007/BFb0100848

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54616-0

  • Online ISBN: 978-3-540-38496-0

  • eBook Packages: Springer Book Archive

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