A stochastic wave equation in dimension 3: Smoothness of the law

Bernoulli

Volumn 10, Issue 1, 2004, Pages 165-186

  Quer Sardanyons, Lluís ^a   Sanz Solé, Marta ^a  

^a UNIVERSITY OF BARCELONA   (Spain)

Author keywords

Malliavin calculus; Stochastic partial differential equations; Wave equation

Indexed keywords

EID: 14844311539     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.3150/bj/1077544607     Document Type: Article

References (8)

1. Dalang, R.C. (1999) Extending the martingale measure stochastic integral with applications to spatially homogeneous s.p.d.e's. Electron. J. Probab., 4(6).
2. Dalang, R.C. and Frangos, N. (1998) The stochastic wave equation in two spatial dimensions. Ann. Probab., 26, 187-212.
3. Lévêque, O. (2001) Hyperbolic Stochastic Partial Differential Equations Driven by Boundary Noises. Doctoral thesis no. 2452, École Polytechnique Fédérale de Switzerland, Lausanne, Switzerland.
4. Márquez-Carreras, D., Mellouk, M. and Sarrà, M. (2001) On stochastic partial differential equations with spatially correlated noise: smoothness of the law. Stochastic Process. Appl., 93, 269-284.
5. Millet, A. and Sanz-Solé, M. (1999) A stochastic wave equation in two space dimensions: smoothness of the law. Ann. Probab., 27, 803-844.
6. Nualart, D. (1995) Malliavin Calculus and Related Topics. New York: Springer-Verlag.
7. Nualart, D. (1998) Analysis on Wiener space and anticipating stochastic calculus. In P. Bernard (ed.), Lecture Notes in Probability Theory and Statistics: École d'Été de Probabilités de Saint Flour XXV-1995, Lecture Notes in Math. 1690, pp. 863-901. Berlin: Springer- Verlag.
8. Quer-Sardanyons, L. and Sanz-Solé, M. (2004) Absolute continuity of the law of the solution to the three-dimensional stochastic wave equation. J. Funct. Anal., 206(1), 1-32.