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Book Review
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Book Information
Author(s):
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.,
US$84.95,
ISBN 978-0849340307
References:
-
- 1.
- V. Bally and E. Pardoux. Malliavin calculus for white noise driven parabolic SPDEs, Potential Anal. 9(1998), 27-64. MR 1644120 (99g:60095)
- 2.
- D. Bell. The Malliavin Calculus, Pitman Monograph 34, Wiley, 1987. MR 902583 (88m:60155)
- 3.
- J.M. Bismut. Large Deviations and the Malliavin Calculus, Prog. Math. 45, Birkhäuser, 1984. MR 755001 (86f:58150)
- 4.
- R.H. Cameron and W.T. Martin. Transformations of Wiener integrals by nonlinear transformations, Trans. Amer. Math. Soc. 66(1949), 253-283. MR 0031196 (11:116b)
- 5.
- R.A. Carmona and B. Rozovskii. Stochastic Partial Differential Equations: Six Perspectives, Math. Surveys and Monographs 44, AMS, 1999. MR 1661761 (99g:60005)
- 6.
- J.M.C. Clark. The representation of functionals of Brownian motion by stochastic integrals, Ann. Math. Statist. 41 (1970), 1282-1295. MR 0270448 (42:5336)
- 7.
- R.C. Dalang. Extending martingale measure stochastic integral with applications to spatially homogeneous s.p.d.e.'s, Elect. J. Probab. 4(1999), paper 6, 1-29. MR 1684157 (2000b:60132)
- 8.
- G. Da Prato and J. Zabczyk. Stochastic Equations in Infinite Dimensions, Cambridge University Press, second ed. (1998). MR 1207136 (95g:60073)
- 9.
- D.A. Dawson. Measure-valued Markov processes, in Ecole d'été de probabilités de Saint Flour XXI, Lecture Notes in Math. 1541, Springer-Verlag, 1993. MR 1242575 (94m:60101)
- 10.
- H. Holden, B. Øksendal, J. Ubøe and T. Zhang. Stochastic Partial Differential Equations, Birkhäuser, 1996. MR 1408433 (98f:60124)
- 11.
- K. Itô. On stochastic differential equations, Mem. Amer. Math. Soc. 4(1951). MR 0040618 (12:724a)
- 12.
- K. Itô. Multiple Wiener integral, J. Math. Soc. Japan 3(1951), 157-169. MR 0044064 (13:364a)
- 13.
- H.H. Kuo. A quarter century of white noise theory, in Quantum Information IV, T. Hida and K. Saitô, eds., World Scientific (2002), pp. 1-37. MR 1947556 (2003k:60001)
- 14.
- S. Kusuoka and D.W. Stroock. Application of the Malliavin calculus, I, in Stochastic Analysis, Proc. Taniguchi Inter. Symp. on Stochastic Analysis, Katata and Kyoto, 1982, ed. K. Itô, Kinokuniya/North-Holland, Tokyo, 1984, pp. 271-306. MR 780762 (86k:60100a)
- 15.
- S. Kusuoka and D.W. Stroock. Application of the Malliavin calculus, II, J. Fac. Sci. Univ. Tokyo IA Math. 32(1985), 1-76. MR 783181 (86k:60100b)
- 16.
- S. Kusuoka and D.W. Stroock. Application of the Malliavin calculus, III, J. Fac. Sci. Univ. Tokyo IA Math. 34(1987), 391-442. MR 914028 (89c:60093)
- 17.
- P. Malliavin. Stochastic calculus of variations and hypoelliptic operators, in Proc. Inter. Symp. on Stoch. Diff. Equations, Kyoto (1976), Wiley, 1978, pp. 195-263. MR 536013 (81f:60083)
- 18.
- P. Malliavin. Stochastic Analysis, Grundlehren der Mathematischen Wissenschaften 313, Springer-Verlag, 1997. MR 1450093 (99b:60073)
- 19.
- Paul Malliavin and Anton Thalmaier. Stochastic Calculus of Variations in Mathematical Finance, Springer, 2006. MR 2189710 (2007b:91002)
- 20.
- M. Métivier. Stochastic partial differential equations in infinite-dimensional spaces, with a preface by G. Da Prato. Scuola Normale Superiore, Pisa, 1988. MR 982268 (90a:60112)
- 21.
- A. Millet and M. Sanz-Solé. A stochastic wave equation in two space dimension: smoothness of the law, Ann. Probab. 27 (1999), 803-844. MR 1698971 (2001e:60130)
- 22.
- D. Nualart. The Malliavin Calculus and Related Topics, 2nd ed., Springer-Verlag, 2006. MR 2200233 (2006j:60004)
- 23.
- D. Ocone. Stochastic calculus of variations for stochastic partial differential equations, J. Funct. Anal. 79(1988), 231-288. MR 953905 (89i:60119)
- 24.
- S. Peszat and J. Zabczyk. Nonlinear stochastic wave and heat equations, Probab. Theory Relat. Fields 116(2000), 421-443. MR 1749283 (2001f:60071)
- 25.
- D.W. Stroock. The Malliavin calculus, a functional analytic approach, J. Functional Anal. 44(1981), 14-171. MR 642917 (83h:60076)
- 26.
- J.B. Walsh. An introduction to Stochastic Partial Differential Equations, in Ecole d'été de probabilités de Saint Flour XIV, Lecture Notes in Math. 1180, Springer-Verlag, 1986. MR 876085 (88a:60114)
- 27.
- S. Watanabe. Lectures on Stochastic Differential Equations and Malliavin Calculus, Tata Institute of Fundamental Research, Springer-Verlag, 1984. MR 742628 (86b:60113)
- 28.
- N. Wiener. Differential space, J. Math. Phys. 2(1923), 131-174.
- 29.
- N. Wiener. The homogeneous chaos, Amer. J. Math. 60(1938), 879-936. MR 1507356
Additional Information:
Reviewer(s):
Donald
Dawson
Affiliation:
Carleton University
Email:
ddawson@math.carleton.ca
Review Information:
Journal:
Bull. Amer. Math. Soc.
44
(2007),
497-504.
MSC
(2000):
Primary 60-02;
Secondary 60H07, 60H15
PII:
S 0273-0979(07)01150-0
Posted:
April 11, 2007
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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