Research partially supported by Seed Grant 958-Math at Boston University
Preview
Unable to display preview. Download preview PDF.
References
R. H. Cameron and R. E. Graves, Additive functionals on a space of continuous functions, Trans. Amer. Math. Soc. 70 (1951), 160–176.
R. H. Cameron and W. T. Martin, Transformation of Wiener integrals under translations, Ann. Math. Stat. 45 (1944), 386–396.
—, The transformation of Wiener integrals by nonlinear transformations, Trans. Amer. Math. Soc. 66 (1949), 253–283.
J.-D. Deuschel and D. W. Stroock, Large deviations, Acad. Press, Boston, 1989.
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.
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.
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.
G. Kallianpur, Stochastic filtering theory, Springer-Verlag, New York, 1980.
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.
R. Liptser and A. Shiriyayev, Statistics of random processes, vol. I&II, Springer-Verlag, New York, 1977.
D. Nualart and E. Pardoux, Stochastic calculus with anticipating integrands, Probab. Th. Rel. Fields 78 (1988), 535–581.
R. Ramer, On nonlinear transformations of Gaussian measures, J. Funct. Analysis 15 (1974), 166–187.
L. A. Shepp, Radon-Nikodym derivatives of Gaussian measures, Ann. Math. Stat. 37 (1966), 321–354.
B. Simon, Functional integration and quantum physics, Acad. Press, New York, 1979.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1992 International Federation for Information Processing
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/BFb0007320
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55292-5
Online ISBN: 978-3-540-47015-1
eBook Packages: Springer Book Archive