Abstract
So far, the Malliavin calculus has been rarely used in articles covering the numerical analysis of stochastic processes, in particular for SPDEs, and we find it appropriate to provide a gentle and self-contained introduction into this theory.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
C. Carstensen, An adaptive mesh-refining algorithm allowing for an H 1 stable L 2 projection onto Courant finite element spaces. Constr. Approx. 20(4), 549–564 (2004)
D.L. Cohn, Measure Theory (Birkhäuser, Boston [u.a.], 1993)
G. Da Prato, J. Zabczyk, Stochastic Equations in Infinite Dimensions. Encyclopedia of Mathematics and Its Applications, vol. 44 (Cambridge University Press, Cambridge, 1992)
A. Grorud, É. Pardoux, Intégrales Hilbertiennes anticipantes par rapport à un processus de Wiener cylindrique et calcul stochastique associé. Appl. Math. Optim. 25(1), 31–49 (1992)
J.A. León, D. Nualart, Stochastic evolution equations with random generators. Ann. Probab. 26(1), 149–186 (1998)
P. Malliavin, Stochastic calculus of variation and hypoelliptic operators, in Proceedings of the International Symposium on Stochastic Differential Equations (Res. Inst. Math. Sci., Kyoto Univ., Kyoto, 1976) (Wiley, New York, 1978), pp. 195–263
D. Nualart, The Malliavin Calculus and Related Topics, 2nd edn. Probability and Its Applications (New York) (Springer, Berlin, 2006)
D. Nualart, Application of Malliavin calculus to stochastic partial differential equations, in A Minicourse on Stochastic Partial Differential Equations. Lecture Notes in Mathematics, vol. 1962 (Springer, Berlin, 2009), pp. 73–109
M. Veraar, The stochastic Fubini theorem revisited. Stochastics 84(4), 543–551 (2012)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Kruse, R. (2014). A Short Review of the Malliavin Calculus in Hilbert Spaces. In: Strong and Weak Approximation of Semilinear Stochastic Evolution Equations. Lecture Notes in Mathematics, vol 2093. Springer, Cham. https://doi.org/10.1007/978-3-319-02231-4_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-02231-4_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-02230-7
Online ISBN: 978-3-319-02231-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)