Malliavin Calculus for White Noise Driven Parabolic SPDEs

Potential Analysis

Volumn 9, Issue 1, 1998, Pages 27-64

  Bally, Vlad ^a,b   Pardoux, Etienne ^c  

^a UNIVERSITÉ DU MAINE   (France)

^b University of Paris VII LPSM partially supported by ERC Starting Grant 680275 MALIG   (France)

^c CNRS   (France)

Author keywords

Malliavin calculus; Space time white noise; Stochastic partial differential equations

Indexed keywords

EID: 0032327769     PISSN: 09262601     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008686922032     Document Type: Article

References (13)

1. Aida, S., Kusuoka, S. and Stroock, D.: 'On the support of Wiener functionals', in: Elworthy, K.D. and Ikeda, N. (eds.), Asymptotic problems in probability theory: Wiener functionals and asymptotics, Pitman Research Notes in Math. 284, Longman Sci. Tech., 1993, pp. 3-34.
2. Ben Arous, G. and Léandre, R.: 'Décroissance exponentielle du noyau de la chaleur sur la diagonale II', Prob. Theory Relat. Fields 90 (1991), 377-402.
3. Carmona, R. and Nualart, D.: 'Random non-linear wave equations: Smoothness of the solution', Probab. Theory Related Fields 79 (1988), 464-508.
4. Donati-Martin, C. and Pardoux, E.: 'White noise driven SPDEs with reflection', Probab. Theory Relat. Fields 95 (1993), 1-24.
5. Ikeda, N. and Watanabe, S.: Stochastic Differential Equations and Diffusion Processes, North-Holland, Amsterdam, 1981.
6. Métivier, M.: Semimartingales, de Gruyter, 1982.
7. Millet, A. and Sanz-Solé, M.: 'Points of positive density for the solution to hyperbolic equations', Potential Analysis 7 (1997), 623-659.
8. Nualart, D.: 'Analysis on Wiener space and anticipating stochastic calculus', in: P. Bernard (ed.), Ecole d'Eté de Probabilités de St Flour 1995, LNM, Springer, to appear.
9. Nualart, D.: The Malliavian Calculus and Related Fields, Springer, 1995.
10. Nualart, D. and Sanz, M.: 'Malliavin Calculus for two-parameter Wiener Functionals', Z. Wahrs. Verw. Geb. 70 (1985), 573-590.
11. Nualart, D. and Zakai, M.: 'Generalized Brownian Functionals and the Solution of a Stochastic Partial Differential Equation', J. of Funct. Anal. 84 (1989), 279-296.
12. Pardoux, E. and Zhang, T.: 'Absolute continuity for the law of the solution of a parabolic SPDE', J. of Funct. Anal. 112 (1993), 447-458.
13. Walsh, J.B.: 'An introduction to stochastic partial differential equations', in Ecole d'Eté de Probabilités de Saint Flour XV, Lecture Notes in Math. 1180, Springer, 1986, pp. 266-437.