Bulletin of the American Mathematical Society

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Book Information:

Author: Dennis R. Bell
Title: The Malliavin calculus
Additional book information: Pitman Monographs and Surveys in Pure and Applied Mathematics, vol. 34, Longman Scientific and Technical, Essex, and John Wiley, New York, 1987, x + 105 pp., $62.95. ISBN 0-582-99486-1.

Jean-Michel Bismut and Dominique Michel, Diffusions conditionnelles. I. Hypoellipticité partielle, J. Functional Analysis 44 (1981), no. 2, 174–211 (French, with English summary). MR 642916, DOI 10.1016/0022-1236(81)90010-0

Jean-Michel Bismut and Dominique Michel, Diffusions conditionnelles. I. Hypoellipticité partielle, J. Functional Analysis 44 (1981), no. 2, 174–211 (French, with English summary). MR 642916, DOI 10.1016/0022-1236(81)90010-0

Bernard Gaveau and Philip Trauber, L’intégrale stochastique comme opérateur de divergence dans l’espace fonctionnel, J. Functional Analysis 46 (1982), no. 2, 230–238 (French, with English summary). MR 660187, DOI 10.1016/0022-1236(82)90036-2

J. J. Kohn, Pseudo-differential operators and hypoellipticity, Partial differential equations (Proc. Sympos. Pure Math., Vol. XXIII, Univ. California, Berkeley, Calif., 1971) Amer. Math. Soc., Providence, R.I., 1973, pp. 61–69. MR 0338592

Dominique Michel, Conditional laws and Hörmander’s condition, Stochastic analysis (Katata/Kyoto, 1982) North-Holland Math. Library, vol. 32, North-Holland, Amsterdam, 1984, pp. 387–408. MR 780766, DOI 10.1016/S0924-6509(08)70401-X

David Nualart and Moshe Zakai, Generalized stochastic integrals and the Malliavin calculus, Probab. Theory Relat. Fields 73 (1986), no. 2, 255–280. MR 855226, DOI 10.1007/BF00339940

D. Nualart and É. Pardoux, Stochastic calculus with anticipating integrands, Probab. Theory Related Fields 78 (1988), no. 4, 535–581. MR 950346, DOI 10.1007/BF00353876

Daniel Ocone, Malliavin’s calculus and stochastic integral representations of functionals of diffusion processes, Stochastics 12 (1984), no. 3-4, 161–185. MR 749372, DOI 10.1080/17442508408833299

É. Pardoux and P. Protter, A two-sided stochastic integral and its calculus, Probab. Theory Related Fields 76 (1987), no. 1, 15–49. MR 899443, DOI 10.1007/BF00390274

Daniel W. Stroock and S. R. Srinivasa Varadhan, Multidimensional diffusion processes, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 233, Springer-Verlag, Berlin-New York, 1979. MR 532498

Ali Süleyman Üstünel, Une extension du calcul d’Itô via le calcul des variations stochastiques, C. R. Acad. Sci. Paris Sér. I Math. 300 (1985), no. 9, 277–279 (French, with English summary). MR 785069

1.

J. M. Bismut and D. Michel, Diffusions conditionnelles. I, J. Funct. Anal. 44 (1981), 174-211. MR 0642916

2.

J. M. Bismut and D. Michel, Diffusions conditionnelles. II, J. Funct. Anal. 45 (1982), 274-292. MR 647076

3.

B. Gaveau and P. Trauber, L'intégrale stochastique comme opérateur de divergence dans l'espace fonctionnel, J. Funct. Artal. 46 (1982), 230-238. MR 660187

4.

J. J. Kohn, Pseudo-differential operators and hypoellipticity, Proc. Sympos. Pure Math., vol. 23, Amer. Math. Soc. Providence, R. I., 1969, pp. 61-69. MR 338592

5.

D. Michel, Conditional laws and Hörmander condition, Taniguchi Symposium, 1982, North-Holland, Amsterdam, 1984, pp. 387-408. MR 780766

6.

D. Nualart and M. Zakai, Generalized stochastic integrals and the Malliavin calculus, Probab. Theory Related Fields 73 (1986), 255-280. MR 855226

7.

D. Nualart and E. Pardoux, Stochastic calculus with anticipating integrands, Probab. Theory Related Fields (to appear). MR 950346

8.

D. Ocone, Malliavin's calculus and stochastic integral representation of functional of diffusion processes, Stochastics 12 (1984), 161-185. MR 749372

9.

E. Pardoux and P. Protter, A two-sided stochastic integral and its calculus, Probab. Theory Related Fields 76 (1987), 15-49. MR 899443

10.

D. W. Stroock and S. R. S. Varadhan, Multidimensional diffusion processes, Springer-Verlag, Berlin and New York, 1979. MR 532498

11.

A. S. Ustunel, Une extension du calcul d'Itô via le calcul stochastique des variations, C. R. Acad. Sci. Paris 300 (1985), 277-279. MR 785069