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Stochastic calculus with anticipation and shift transformations of wiener's measure

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Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 176))

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Research partially supported by Seed Grant 958-Math at Boston University

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References

  1. R. H. Cameron and R. E. Graves, Additive functionals on a space of continuous functions, Trans. Amer. Math. Soc. 70 (1951), 160–176.

    Google Scholar 

  2. R. H. Cameron and W. T. Martin, Transformation of Wiener integrals under translations, Ann. Math. Stat. 45 (1944), 386–396.

    Google Scholar 

  3. —, The transformation of Wiener integrals by nonlinear transformations, Trans. Amer. Math. Soc. 66 (1949), 253–283.

    Google Scholar 

  4. J.-D. Deuschel and D. W. Stroock, Large deviations, Acad. Press, Boston, 1989.

    Google Scholar 

  5. I. V. Girsanov, On transforming a certain class of stochastic processes by absolutely continuous substitution of measures, Theory Probab. Its Appl. 5 (1960), 285–301.

    Google Scholar 

  6. I. C. Gohberg and M. G. Krein, Theory and applications of Volterra operators in Hilbert spaces, Am. Math. Soc., Transl., vol. vol. 24, Am. Math. Soc., Providence, RI, 1970.

    Google Scholar 

  7. Yu. Kabanov and A. Skorohod [Ю. Кабалоо и А. Скороход], Расщирепщые Стохастические Иитеграяы [Extended Stochastic Integrals], Труды Щколы-Семипара по Теории Случайиых Процессоб [Proc. of Workshop on Stochastic Processes] (Vilnius, Lithuania), 1975.

    Google Scholar 

  8. G. Kallianpur, Stochastic filtering theory, Springer-Verlag, New York, 1980.

    Google Scholar 

  9. Sh. Kusuoka, The nonlinear transformation of Gaussian measure on Banach space and its absolute continuity (I), J. Fac. Sci. Univ. Tokyo, Sect. IA 29 (1982), 567–598.

    Google Scholar 

  10. R. Liptser and A. Shiriyayev, Statistics of random processes, vol. I&II, Springer-Verlag, New York, 1977.

    Google Scholar 

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

    Google Scholar 

  12. R. Ramer, On nonlinear transformations of Gaussian measures, J. Funct. Analysis 15 (1974), 166–187.

    Google Scholar 

  13. L. A. Shepp, Radon-Nikodym derivatives of Gaussian measures, Ann. Math. Stat. 37 (1966), 321–354.

    Google Scholar 

  14. B. Simon, Functional integration and quantum physics, Acad. Press, New York, 1979.

    Google Scholar 

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Boris L. Rozovskii Richard B. Sowers

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© 1992 International Federation for Information Processing

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Enchev, O. (1992). Stochastic calculus with anticipation and shift transformations of wiener's measure. In: Rozovskii, B.L., Sowers, R.B. (eds) Stochastic Partial Differential Equations and Their Applications. Lecture Notes in Control and Information Sciences, vol 176. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0007320

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  • DOI: https://doi.org/10.1007/BFb0007320

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