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On generalized multiple stochastic integrals and multiparameter anticipative calculus

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Stochastic Analysis and Related Topics II

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1444))

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References

  1. BERGER, M., MIZEL, V. An extension of the stochastic integral. Ann. Probab. 10, 435–450, (1982).

    Article  MathSciNet  MATH  Google Scholar 

  2. CHENTSOV, N. N., Wiener random fields depending on several parameters. Dokl. Akad. Nauk. SSSR 106, 607, 609 (1956).

    MathSciNet  Google Scholar 

  3. FÖLLMER, H. Calcul d’Itô sans probabilités. Séminaire de Probabilités XV. Lecture Notes in Math. 850, 143–150. Springer Verlag (1981).

    Google Scholar 

  4. MEYER, P. A. Transformations de Riesz pour les lois Gaussiennes. Séminaire de Probabilités XVIII. Lecture Notes in Math 1059, 179–193. Springer Verlag (1984).

    Google Scholar 

  5. NUALART, D., ZAKAI, M. Generalized stochastic integrals and the Malliavin Calculus. Probab. Theory and Related Fields 73, 255–280 (1986).

    Article  MathSciNet  MATH  Google Scholar 

  6. NUALART, D., ZAKAI, M. Generalized Multiple stochastic integrals and the representation of Wiener functionals. Stochastics 23, 311–330 (1988).

    Article  MathSciNet  MATH  Google Scholar 

  7. NUALART, D., PARDOUX, E. Stochastic Calculus with Anticipating integrands. Probab. Theory and Related Fields 78, 535–581 (1988).

    Article  MathSciNet  MATH  Google Scholar 

  8. OCONE, D. Malliavin Calculus and stochastic integral representation of functionals of diffusion processes. Stochastics 12, 161–185 (1984).

    Article  MathSciNet  MATH  Google Scholar 

  9. OGAWA, D. Quelques propiétés de l’intégrale stochastique du type noncausal. Japan Journal of Appl. Math. 1, 405–416 (1988).

    Article  MATH  Google Scholar 

  10. RAMER, R. On non-linear transformations of Gaussian measures. J. Funct. Anal. 15, 166–187 (1974).

    Article  MathSciNet  MATH  Google Scholar 

  11. SHIGEKAWA, I. Derivatives of Wiener functionals and absolute continuity of induced measures. J. Math. Kyoto Univ. 20–2, 263–289 (1980).

    MathSciNet  MATH  Google Scholar 

  12. SEKIGUCHI, T., SHIOTA, Y. L2-theory of noncausal stochastic integrals. Math. Rep. Toyama Univ. 8, 119–195 (1985).

    MathSciNet  MATH  Google Scholar 

  13. SKOROHOD, A. V. On a generalization of a stochastic integral. Theory of Probab. and Appl. 20, 219–233 (19875).

    Google Scholar 

  14. USTUNEL, A. S. Representation of the Distributions on Wiener Space and Stochastic Calculus of Variations. J. of Functional Analysis, 70, 126–139 (1987).

    Article  MathSciNet  MATH  Google Scholar 

  15. USTUNEL, A. S. The Itô Formula for Anticipative Processes with Nonmonotonous Time Scale via the Malliavin Calculus. Probab. Theory and Related Fields 79, 249–269 (1988).

    Article  MathSciNet  MATH  Google Scholar 

  16. WATANABE, S. Stochastic differential equations and Malliavin Calculus. Tata Inst. of Fundamental Research. Springer Verlag (1984).

    Google Scholar 

  17. WONG, E., ZAKAI, M. Differentiation formulas for stochastic integrals in the plane. Stochastic Proc. and their Appl. 6 339–349 (1978).

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Departament de Matemàtiques Facultat de Ciències, Universitat Autònoma de Barcelona, 08193, Bellaterra (Barcelona), Spain

    Maria Jolis

  2. Facultat de Matemàtiques, Universitat de Barcelona, Gran Via, 585, 08007, Barcelona, Spain

    Marta Sanz

Authors
  1. Maria Jolis
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  2. Marta Sanz
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Hayri Korezlioglu Ali Suleyman Ustunel

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© 1990 Springer-Verlag

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Jolis, M., Sanz, M. (1990). On generalized multiple stochastic integrals and multiparameter anticipative calculus. In: Korezlioglu, H., Ustunel, A.S. (eds) Stochastic Analysis and Related Topics II. Lecture Notes in Mathematics, vol 1444. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083614

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  • DOI: https://doi.org/10.1007/BFb0083614

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53064-0

  • Online ISBN: 978-3-540-46596-6

  • eBook Packages: Springer Book Archive

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