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Some relations among classes of σ-fields on Wiener space
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  • Published: March 1990

Some relations among classes of σ-fields on Wiener space

  • D. Nualart1,
  • A. S. Ustunel2 &
  • M. Zakai3 

Probability Theory and Related Fields volume 85, pages 119–129 (1990)Cite this article

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  • 11 Citations

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Summary

In this work we study sigma fields and their tangent spaces on the Wiener space which are invariant in some sense with respect to the basic operators of the Malliavin Calculus.

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References

  1. Airault, H., Malliavin, P.: Intégration géometrique sur l'espace de Wiener. Bull. Sci. Math., II. Sér.112, 1–52 (1988)

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  2. Ikeda, N., Watanabe, S.: An introduction to Malliavin's Calculus. Proceedings of the Taniguchi International Symposium on Stochastic Analysis, Katata-Kyoto, 1982, pp. 1–52. Kinokuniya/North-Holland 1984

  3. D. Nualart, M. Zakai, Generalized stochastic integrals and the Malliavin Calculus. Probab. Th. Rel. Fields73, 255–280 (1986)

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  4. Nualart, D., Zakai, M.: The partial Malliavin Calculus. Séminaire de Probabilités XXIII, (Lect. Notes Math., vol. 1372, pp. 362–381) Berlin Heidelberg New York: Springer 1989

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  5. Ustunel, A.S., Zakai, M.: On independence and conditioning on Wiener space. Ann. Probab.17, 1441–1453 (1989)

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  6. Ustunel, A.S., Zakai, M.: On the structure of independence on Wiener space. J. Funct. Anal. (to appear)

  7. Watanabe, S.: Lectures on stochastic differential equations and Malliavin Calculus. Tata Institute of Fundamental Research. Berlin Heidelberg New York: Springer 1984

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Author information

Authors and Affiliations

  1. Facultat de Matemàtiques, Universitat de Barcelona, Gran Via, 585, E-08007, Barcelona, Spain

    D. Nualart

  2. No. 2, Boulevard Auguste Blanqui, F-75013, Paris, France

    A. S. Ustunel

  3. Department of Electrical Engineering, Technion-Israel Institute of Technology, 32000, Haifa, Israel

    M. Zakai

Authors
  1. D. Nualart
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  2. A. S. Ustunel
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  3. M. Zakai
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Cite this article

Nualart, D., Ustunel, A.S. & Zakai, M. Some relations among classes of σ-fields on Wiener space. Probab. Th. Rel. Fields 85, 119–129 (1990). https://doi.org/10.1007/BF01377633

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  • Received: 24 May 1989

  • Revised: 11 October 1989

  • Issue Date: March 1990

  • DOI: https://doi.org/10.1007/BF01377633

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Keywords

  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Tangent Space
  • Basic Operator
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