Skip to Main Content

Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

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

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

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: Marta Sanz-Solé
Title: Malliavin calculus with applications to stochastic partial differential equations
Additional book information: Fundamental Sciences, EPFL Press, Lausanne, distributed by CRC Press, Boca Raton, FL, 2005, viii+162 pp., ISBN 978-0849340307, US$84.95$

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

  • Vlad Bally and Etienne Pardoux, Malliavin calculus for white noise driven parabolic SPDEs, Potential Anal. 9 (1998), no. 1, 27–64. MR 1644120, DOI 10.1023/A:1008686922032
  • Denis R. Bell, The Malliavin calculus, Pitman Monographs and Surveys in Pure and Applied Mathematics, vol. 34, Longman Scientific & Technical, Harlow; John Wiley & Sons, Inc., New York, 1987. MR 902583
  • Jean-Michel Bismut, Large deviations and the Malliavin calculus, Progress in Mathematics, vol. 45, Birkhäuser Boston, Inc., Boston, MA, 1984. MR 755001
  • R. H. Cameron and W. T. Martin, The transformation of Wiener integrals by nonlinear transformations, Trans. Amer. Math. Soc. 66 (1949), 253–283. MR 31196, DOI 10.1090/S0002-9947-1949-0031196-6
  • Rene A. Carmona and Boris Rozovskii (eds.), Stochastic partial differential equations: six perspectives, Mathematical Surveys and Monographs, vol. 64, American Mathematical Society, Providence, RI, 1999. MR 1661761, DOI 10.1090/surv/064
  • J. M. C. Clark, The representation of functionals of Brownian motion by stochastic integrals, Ann. Math. Statist. 41 (1970), 1282–1295. MR 270448, DOI 10.1214/aoms/1177696903
  • Robert C. Dalang, Extending the martingale measure stochastic integral with applications to spatially homogeneous s.p.d.e.’s, Electron. J. Probab. 4 (1999), no. 6, 29. MR 1684157, DOI 10.1214/EJP.v4-43
  • Giuseppe Da Prato and Jerzy Zabczyk, Stochastic equations in infinite dimensions, Encyclopedia of Mathematics and its Applications, vol. 44, Cambridge University Press, Cambridge, 1992. MR 1207136, DOI 10.1017/CBO9780511666223
  • Donald A. Dawson, Measure-valued Markov processes, École d’Été de Probabilités de Saint-Flour XXI—1991, Lecture Notes in Math., vol. 1541, Springer, Berlin, 1993, pp. 1–260. MR 1242575, DOI 10.1007/BFb0084190
  • Helge Holden, Bernt Øksendal, Jan Ubøe, and Tusheng Zhang, Stochastic partial differential equations, Probability and its Applications, Birkhäuser Boston, Inc., Boston, MA, 1996. A modeling, white noise functional approach. MR 1408433, DOI 10.1007/978-1-4684-9215-6
  • Kiyosi Ito, On stochastic differential equations, Mem. Amer. Math. Soc. 4 (1951), 51. MR 40618
  • Kiyosi Itô, Multiple Wiener integral, J. Math. Soc. Japan 3 (1951), 157–169. MR 44064, DOI 10.2969/jmsj/00310157
  • Hui-Hsiung Kuo, A quarter century of white noise theory, Quantum information, IV (Nagoya, 2001) World Sci. Publ., River Edge, NJ, 2002, pp. 1–37. MR 1947556, DOI 10.1142/9789812777324_{0}001
  • Shigeo Kusuoka and Daniel Stroock, Applications of the Malliavin calculus. I, Stochastic analysis (Katata/Kyoto, 1982) North-Holland Math. Library, vol. 32, North-Holland, Amsterdam, 1984, pp. 271–306. MR 780762, DOI 10.1016/S0924-6509(08)70397-0
  • Shigeo Kusuoka and Daniel Stroock, Applications of the Malliavin calculus. I, Stochastic analysis (Katata/Kyoto, 1982) North-Holland Math. Library, vol. 32, North-Holland, Amsterdam, 1984, pp. 271–306. MR 780762, DOI 10.1016/S0924-6509(08)70397-0
  • S. Kusuoka and D. Stroock, Applications of the Malliavin calculus. III, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 34 (1987), no. 2, 391–442. MR 914028
  • Paul Malliavin, Stochastic calculus of variation and hypoelliptic operators, Proceedings of the International Symposium on Stochastic Differential Equations (Res. Inst. Math. Sci., Kyoto Univ., Kyoto, 1976) Wiley, New York-Chichester-Brisbane, 1978, pp. 195–263. MR 536013
  • Paul Malliavin, Stochastic analysis, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 313, Springer-Verlag, Berlin, 1997. MR 1450093, DOI 10.1007/978-3-642-15074-6
  • Paul Malliavin and Anton Thalmaier, Stochastic calculus of variations in mathematical finance, Springer Finance, Springer-Verlag, Berlin, 2006. MR 2189710
  • M. Métivier, Stochastic partial differential equations in infinite-dimensional spaces, Scuola Normale Superiore di Pisa. Quaderni. [Publications of the Scuola Normale Superiore of Pisa], Scuola Normale Superiore, Pisa, 1988. With a preface by G. Da Prato. MR 982268
  • Annie Millet and Marta Sanz-Solé, A stochastic wave equation in two space dimension: smoothness of the law, Ann. Probab. 27 (1999), no. 2, 803–844. MR 1698971, DOI 10.1214/aop/1022677387
  • David Nualart, The Malliavin calculus and related topics, 2nd ed., Probability and its Applications (New York), Springer-Verlag, Berlin, 2006. MR 2200233
  • Daniel Ocone, Stochastic calculus of variations for stochastic partial differential equations, J. Funct. Anal. 79 (1988), no. 2, 288–331. MR 953905, DOI 10.1016/0022-1236(88)90015-8
  • Szymon Peszat and Jerzy Zabczyk, Nonlinear stochastic wave and heat equations, Probab. Theory Related Fields 116 (2000), no. 3, 421–443. MR 1749283, DOI 10.1007/s004400050257
  • Daniel W. Stroock, The Malliavin calculus, a functional analytic approach, J. Functional Analysis 44 (1981), no. 2, 212–257. MR 642917, DOI 10.1016/0022-1236(81)90011-2
  • John B. Walsh, An introduction to stochastic partial differential equations, École d’été de probabilités de Saint-Flour, XIV—1984, Lecture Notes in Math., vol. 1180, Springer, Berlin, 1986, pp. 265–439. MR 876085, DOI 10.1007/BFb0074920
  • S. Watanabe, Lectures on stochastic differential equations and Malliavin calculus, Tata Institute of Fundamental Research Lectures on Mathematics and Physics, vol. 73, Published for the Tata Institute of Fundamental Research, Bombay; by Springer-Verlag, Berlin, 1984. Notes by M. Gopalan Nair and B. Rajeev. MR 742628
  • 28.
    N. Wiener. Differential space, J. Math. Phys. 2(1923), 131-174.
  • Norbert Wiener, The Homogeneous Chaos, Amer. J. Math. 60 (1938), no. 4, 897–936. MR 1507356, DOI 10.2307/2371268

  • Review Information:

    Reviewer: Donald Dawson
    Affiliation: Carleton University
    Email: ddawson@math.carleton.ca
    Journal: Bull. Amer. Math. Soc. 44 (2007), 497-504
    Published electronically: April 11, 2007
    Review copyright: © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.