Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


Full text of review: PDF   This review is available free of charge.
Book Information:

Author: Paul Malliavin
Title: Stochastic analysis
Additional book information: Springer, 1997, 343+xi pp., ISBN 3-540-57024-1, $125.00

References [Enhancements On Off] (What's this?)

  • 1. Jean-Michel Bismut, ``Large Deviations and the Malliavin Calculus,'' Birkhauser, Boston/Basel/Stuttgart, 1984. MR 86f:58150
  • 2. Denis R. Bell, ``The Malliavin Calculus,'' (Pitman monographs and surveys in pure and applied mathematics; 34), Longman Scientific & Technical, Harlow; John Wiley & Sons, Inc., New York, 1987. MR 88m:60155
  • 3. -, ``Degenerate Stochastic Differential Equations and Hypoellipticity,'' (Pitman monographs and surveys in pure and applied mathematics; 79), Longman, Essex, England, 1995. CMP 98:01
  • 4. Nicolas Bouleau and Francis Hirsch, ``Dirichlet Forms and Analysis on Wiener Space'', (Studies in Mathematics 14), de Gruyter, Berlin-New York, 1991. MR 93e:60107
  • 5. R. H. Cameron, The first variation of an indefinite Wiener integral, Proc. A.M.S., Vol 2. (1951), 914 - 924. MR 13:659b
  • 6. R. H. Cameron and W. T. Martin, Transformations of Wiener integrals under translations, Annals of Math., 45, No. 2 (1944), 386 -396. MR 6:5f
  • 7. R. H. Cameron and W. T. Martin, Transformations of Wiener integrals under a general class of linear transformations, Trans. Amer. Math. Soc. 58, (1945) 184 - 219. MR 7:127c
  • 8. R. H. Cameron and W. T. Martin, The transformation of Wiener integrals by non-linear transformations, Trans. Amer. Math. Soc. 66 (1949), 253 - 283. MR 11:116b
  • 9. B. K. Driver, Towards calculus and geometry on path spaces, in ``Stochastic Analysis, Summer Research Institute on Stochastic Analysis,'' July 11-30, 1993, Cornell University, (Eds. M. Cranston and M. Pinsky), Proceedings of Symposia in Pure Mathematics, Vol. 57, American Mathematical Society, Rhode Island, 1995, p. 405-422. MR 96e:60097
  • 10. I. V. Girsanov, On transforming a certain class of stochastic processes by absolutely continuous substitution of measures, Theory Probab. Appl. 5 (1960), 285 - 301. MR 24:A2986
  • 11. James Glimm and Arthur Jaffe, ``Quantum physics. A functional integral point of view.'' Second edition. Springer-Verlag, New York-Berlin, 1987. MR 89k:81001
  • 12. L. Gross, Abstract Wiener Spaces, Proc. 5th. Berkeley Symposium Math. Stat. Prob. 2, (1965), 31 - 42.
  • 13. L. Gross, Potential theory on Hilbert space, J. Func. Anal. 1, 123 - 181, (1967). MR 37:3331
  • 14. N. Ikeda and S. Watanabe, ``Stochastic differential equations and diffusion processes,'' 2nd ed., North-Holland Publishing Co., Amsterdam/Oxford/New York, 1989. MR 90m:60069
  • 15. H-H. Kuo, ``Gaussian measures in Banach spaces,'' Lecture notes in Mathematics, 463, Springer-Verlag, Berlin-New York, 1975. MR 57:1628
  • 16. S. Kusuoka and D. Stroock, Applications of the Malliavin Calculus, Part I, Proc. Int. Symp. S.D.E. Kyoto, (1976) 271 - 306, North-Holland, Amsterdam-New York, 1984. MR 86k:60100a
  • 17. -, Applications of the Malliavin Calculus, Part II, J. Fac. Sci. Univ. Tokyo, Sect IA, Math, Vol. 32 (1985), 1-76. MR 86k:60100b
  • 18. P. Malliavin, Geometrie differentielle stochastique, Montreal: Presses de l' Universite de Montreal, 1978. MR 81d:60077
  • 19. -, Stochastic calculus of variation and hypoelliptic operators, Proc. Int. Symp. S.D.E. Kyoto, (1976) 195 - 263, Wiley and Sons, New York 1978. MR 81f:60083
  • 20. -, $C^{k}$-hypoellipticity with degeneracy, Stochastic Analysis, ed. by A. Friedman and M. Pinsky, 199-214, 321-340, Academic Press, New York, 1978. MR 80i:58045a
  • 21. G. Maruyama, Notes on Wiener integrals, Kodai Math. Seminar Rep. 3 (1950), 41 -44. MR 12:343d
  • 22. J. R. Norris, Simplified Malliavin calculus, Seminaire de Probabilites XX 1984/85 (ed. par J. Azema et M. Yor), Lect. Notes in Math., 1204, 101-130, Springer-Verlag, Berlin, 1986. MR 89f:60058
  • 23. D. Nualart, ``The Malliavin calculus and related topics,'' in Probability and its Applications. Springer-Verlag, New York, 1995. MR 96k:60130
  • 24. I. E. Segal, Tensor algebras over Hilbert spaces, I. Trans. Amer. Math. Soc. 81 (1956), 106-134. MR 17:880d
  • 25. -, Distributions in Hilbert space and canonical systems of operators, Trans. Amer. Math. Soc. 88 (1958), 12-41. MR 21:1545
  • 26. -, Absolute continuity of probability laws of Wiener functionals, Proc. Japan Acad., 54-A, 230-233 (1978). MR 81m:60097
  • 27. -, Derivatives of Wiener functionals and absolute continuity of induced measures, J. Math. Kyoto Univ. 20-2, 263-289 (1980). MR 83g:60051
  • 28. D. W. Stroock, The Malliavin calculus and its application to second order parabolic differential operators, I, II, Math. Systems Theory 14, 25-65 and 141-171 (1981). MR 84d:60092a, MR 84d:60092b
  • 29. -, The Malliavin calculus, a functional analytic approach, J. Funct. Anal., 44, 212-257 (1981). MR 83h:60076
  • 30. S. Watanabe, ``Lectures on Stochastic Differential Equations and Malliavin Calculus, (Tata Institute of Fundamental Research: Lectures given at Indian Institute of Science, Bangalore), Springer-Verlag, Berlin-New York, 1984. MR 86b:60113
  • 31. N. Wiener, Differential space, J. Math. Phys. 2, 131-174 (1923).

Review Information:

Reviewer: Bruce K. Driver
Affiliation: University of California, San Diego
Email: driver@euclid.ucsd.edu
Journal: Bull. Amer. Math. Soc. 35 (1998), 99-104
MSC (1991): Primary 60H07; Secondary 31C15, 60H30
DOI: https://doi.org/10.1090/S0273-0979-98-00739-3
Review copyright: © Copyright 1998 American Mathematical Society
American Mathematical Society