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Applications of anticipating stochastic calculus to stochastic differential equations

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Bibliography

  1. R.A. Adams: Sobolev Spaces. Acad. Press 1975.

    Google Scholar 

  2. J.M. Bismut: A generalized Itô formula and some other properties of stochastic flows Z. Wahrscheinlichkeitstheor. Verw. Geb. 55, 331–350, 1981.

    Article  MathSciNet  MATH  Google Scholar 

  3. J.M. Bismut, D. Michel: Diffusions conditionnelles J. Funct. Anal. 44, 1981, 174–211 and 45, 274–292, 1982..

    Article  MathSciNet  MATH  Google Scholar 

  4. R. Buckdahn: Quasilinear partial stochastic differential equations without nonanticipation requirement. Preprint 176, Humbolt Universität, Berlin, 1988.

    Google Scholar 

  5. R. Buckdahn: Skorohod’s integral and linear stochastic differential equations. Preprint 1843, Humbolt Universität, Berlin, 1988.

    Google Scholar 

  6. H. Kunita: Stochastic differential equations and stochastic flows of diffeomorphisms, Ecole d’été de Probabilité de St. Flour XII, Lecture Notes in Math. 1097, Springer 1982.

    Google Scholar 

  7. H.H.Kuo: Gaussian measures on Banach spaces, Lecture Notes in Math. 463 Springer 1975.

    Google Scholar 

  8. S.Kusuoka: The nonlinear transformation of Gaussian measure on Banach space and its absolute continuity, J.Fac. Sci. Univ. Tokyo Sec. IA, 567–597, 1982.

    Google Scholar 

  9. C. Martias: Une formule d’Itô-Ventsell pour les processus anticipatifs. Preprint.

    Google Scholar 

  10. D.Nualart: Non causal stochastic integrals and calculus, in Stochastic Analysis and Related Topics, H. Korezlioglu & A.S. Ustunel Eds., Lecture Notes in Math. 1316, 80–129, 1988.

    Google Scholar 

  11. D. Nualart, E. Pardoux: Stochastic calculus with anticipating integrands, Probab. Th. Rel. Fields 78, 535–581, 1988.

    Article  MathSciNet  MATH  Google Scholar 

  12. D. Nualart, E. Pardoux: Boundary value problems for stochastic differential equations, Preprint.

    Google Scholar 

  13. D. Nualart, M. Zakai: Generalized stochastic integrals and the Malliavin Calculus, Probab. Th. Rel. Fields 73, 255–280, 1986.

    Article  MathSciNet  MATH  Google Scholar 

  14. D. Nualart, M.Zakai: The partial Malliavin calculus, Preprint.

    Google Scholar 

  15. D. Ocone, E. Pardoux: A generalized Itô-Ventzell formula. Application to a class of anticipating SDEs, Ann. I H P 25, 39–71, 1989.

    MathSciNet  MATH  Google Scholar 

  16. D. Ocone, E. Pardoux: Bilinear SDEs with boundary conditions, Probab. Th. Rel. Fields, to appear.

    Google Scholar 

  17. E. Pardoux, P. Protter: Stochastic Volterra equations with anticipating coefficients, Ann. Probab. to appear.

    Google Scholar 

  18. R. Ramer: On nonlinear transformations of Gaussian measures, J. Funct. Anal. 15, 166–187, 1974.

    Article  MathSciNet  MATH  Google Scholar 

  19. Y. Shiota: A linear SDE contraining the extended Itô integral, Math. Rep. Toyama U. 9, 43–65, 1986.

    MathSciNet  MATH  Google Scholar 

  20. A.V. Skorohod: On a generalization of a stochastic integral, Theory Probab. Appl. 20, 219–233, 1975.

    Article  MathSciNet  Google Scholar 

  21. A.S. Ustunel: Some comments on the filtering of diffusions and the Malliavin Calculus, in Stochastic Analysis and Related Topics, H. Korezlioglu & A.S. Ustunel Eds., Lecture Notes in Math. 1316, 247–266, 1988.

    Google Scholar 

  22. A. S. Ustunel: The Itô formula for anticipative processes with nonmonotonous time via the Malliavin calculus, Probab. Th. Rel. Fields 79, 249–269, 1988.

    Article  MathSciNet  MATH  Google Scholar 

  23. Huang Zhiyuan: On the generalized sample solutions of stochastic boundary value problems, Stochastics 11, 237–248, 1984.

    Article  MathSciNet  MATH  Google Scholar 

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Hayri Korezlioglu Ali Suleyman Ustunel

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© 1990 Springer-Verlag

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Pardoux, E. (1990). Applications of anticipating stochastic calculus to stochastic differential equations. 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/BFb0083610

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  • DOI: https://doi.org/10.1007/BFb0083610

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53064-0

  • Online ISBN: 978-3-540-46596-6

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