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Book Information

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

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).

Reviewer(s):
Bruce K. Driver
Affiliation: University of California, San Diego
Email: driver@euclid.ucsd.edu

MSC (1991): Primary 60H07; Secondary 31C15, 60H30
DOI: 10.1090/S0273-0979-98-00739-3
PII: S 0273-0979(98)00739-3
Copyright of article: Copyright 1998, American Mathematical Society

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ISSN 1088-9485(e) ISSN 0273-0979(p)

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