Existence and Smoothness of the Density for Spatially Homogeneous SPDEs
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Bouleau, N., Hirsch, F.: Dirichlet forms and analysis on Wiener space. Walter de Gruyter, Berlin (1991)
Carmona, R., Nualart, D.: Random nonlinear wave equations: smoothness of the solutions. Probab. Theory Related Fields 79(4), 469–508 (1988)
Dalang, R.C.: Extending martingale measure stochastic integral with applications to spatially homogeneous S. P. D. E’s. Electron. J. Probab. 4(6), 29 (1999) (electronic)
Dalang, R.C., Frangos, N.E.: The stochastic wave equation in two spatial dimensions. Ann. Probab. 26(1), 187–212 (1998)
Da Prato, G., Zabczyk, J.: Stochastic equations in infinite dimensions. Encyclopedia of mathematics and its applications, vol. 44. Cambridge University Press, Cambridge (1992)
Lévêque, O.: Hyperbolic stochastic partial differential equations driven by boundary noises. Ph.D. thesis, EPFL (2001)
Márquez-Carreras, D., Mellouk, M., Sarrà, M.: On stochastic partial differential equations with spatially correlated noise: smoothness of the law. Stochastic Process. Appl. 93, 269–284 (2001)
Millet, A., Sanz-Solé, M.: A stochastic wave equation in two space dimensions: smoothness of the law. Ann. Probab. 27(2), 803–844 (1999)
Nualart, D.: The Malliavin calculus and related topics, 2nd edn. Springer, Berlin (2006)
Peszat, S.: The Cauchy problem for a nonlinear stochastic wave equation in any dimension. J. Evol. Equ. 2(3), 383–394 (2002)
Peszat, S., Zabczyk, J.: Nonlinear stochastic wave and heat equations. Probab. Theory Related Fields 116(3), 421–443 (2000)
Quer-Sardanyons, L.: The stochastic wave equation: study of the law and approximations. Ph.D. thesis, Universitat de Barcelona (2005)
Quer-Sardanyons, L., Sanz-Solé, M.: Absolute continuity of the law of the solution to the 3-dimensional stochastic wave equation. J. Funct. Anal. 206(1), 1–32 (2004)
Quer-Sardanyons, L., Sanz-Solé, M.: A stochastic wave equation in dimension 3: smoothness of the law. Bernoulli 10(1), 165–186 (2004)
Sanz-Solé, M.: Malliavin calculus. With applications to stochastic partial differential equations. Fundamental Sciences. EPFL Press, Lausanne (2005)
Schwartz, D.: Théorie des distributions. Hermann, Paris (1966)
Walsh, J.B.: An introduction to stochastic partial differential equations. In: Hennequin, P.L. (ed.) École d’été de probabilités de Saint-Flour XIV – 1984. Lect. Notes Math. vol. 1180, pp. 265–437. Springer, Berlin (1986)