On the Uniform Integrability of the Radon-Nikodym Densities for Wiener Measure

Journal of Functional Analysis

Volumn 159, Issue 2, 1998, Pages 642-663

  Ustunel A S ^a   Zakai, M ^b  

^a TELECOM PARISTECH   (France)

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040086042     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.1998.3320     Document Type: Article

References (23)

1. Beckenbach E. F., Bellman R. Inequalities. Ergeb. Math. Grenzgeb. 30:1983;Springer-Verlag, Berlin/New York.
2. Cameron R. H., Martin W. T. Transformation of Wiener integral under translation. Ann. Math. 45:1944;386-396.
3. Cameron R. H., Martin W. T. The transformation of Wiener integrals by nonlinear transformation. Trans. Amer. Math. Soc. 66:1949;253-283.
4. Cruzeiro A. B. Equations différentielles sur l'espace de Wiener et formules de Cameron Martin non linéaires. J. Funct. Anal. 54:1983;206-227.
5. Dunford N., Schwartz J. T. Linear Operations. 1957;Interscience, New York.
6. Gross L. Abstract Wiener spaces. Proc. 5th Berkely Symp. Math. Stat. Probab., Part 1. 1965;Univ. Calif. Press, Berkeley.
7. Itô K., Nisio M. On the convergence of sums of independent Banach space valued random variables. J. Math. 5:1968;35-48.
8. Kailath T., Zakai M. Absolute continuity and Radon-Nikodym derivatives for certain measures relative to Wiener measure. Ann. Math. Stat. 42:1971;130-140.
9. Kusuoka S. The nonlinear transformation of Gaussian measure on Banach space and its absolute continuity. J. Fac. Sci. Tokyo Univer. Sect. 1.A. 29:1982;567-590.
10. Kusuoka S. Analysis on Wiener spaces, I. Nonlinear maps. J. Funct. Anal. 98:1991;122-168.
11. Kusuoka S. Analysis on Wiener spaces, II. Differential forms. J. Funct. Anal. 103:1992;229-274.
12. Malliavin P. Stochastic Analysis. 1997;Springer-Verlag, Berlin/New York.
13. Ramer R. On nonlinear transformations of Gaussian measures. J. Funct. Anal. 15:1974;166-187.
14. Schwartz J. Nonlinear Functional Analysis. 1969;Gordon & Breach, New York.
15. Simon B. Trace Ideals and Their Applications. London Math. Soc. Lect. Note Ser. 35:1979;Cambridge Univ. Press, Cambridge.
16. Üstünel A. S. Intégrabilité exponentielle de fonctionnelles de Wiener. C.R. Acad. Sc. Paris Sér. I Math. 315:1992;279-282.
17. Üstünel A. S., Zakai M. Transformation of Wiener measure under anticipative flows. Probab. Theory Related Fields. 93:1992;91-136.
18. Üstünel A. S., Zakai M. Random rotation of the Wiener path. Probab. Theory Related Fields. 103:1995;409-430.
19. Üstünel A. S. Some exponential moment inequalities for the Wiener space. J. Funct. Anal. 136:1996;154-171.
20. Üstünel A. S. An Introduction to Analysis on Wiener Space. Lecture Notes in Math. 1610:1996;Springer-Verlag, Berlin/New York.
21. Üstünel A. S., Zakai M. Transformation of Wiener measure under non-invertible shifts. Probab. Theory Related Fields. 99:1994;485-500.
22. Üstünel A. S., Zakai M. Measures induced on Wiener space by monotone shifts. Probab. Theory Related Fields. 105:1996;545-563.
23. Vainberg M. M. Variational Method and Method of Monotone Operators in the Theory of Nonlinear Equations. 1973;Wiley, New York.