On the density for the solution of a Burgers-type SPDE
Morien, Pierre-Luc
Annales de l'I.H.P. Probabilités et statistiques, Tome 35 (1999), p. 459-482 / Harvested from Numdam
Publié le : 1999-01-01
@article{AIHPB_1999__35_4_459_0,
     author = {Morien, Pierre-Luc},
     title = {On the density for the solution of a Burgers-type SPDE},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {35},
     year = {1999},
     pages = {459-482},
     mrnumber = {1702238},
     zbl = {0935.60046},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_1999__35_4_459_0}
}
Morien, Pierre-Luc. On the density for the solution of a Burgers-type SPDE. Annales de l'I.H.P. Probabilités et statistiques, Tome 35 (1999) pp. 459-482. http://gdmltest.u-ga.fr/item/AIHPB_1999__35_4_459_0/

[1] V. Bally, I. Gyöngy and E. Pardoux, White-noise driven parabolic SPDEs with measurable drift, J. Funct. Anal. 120 (2) (1994) 484-510. | MR 1266318 | Zbl 0801.60049

[2] V. Bally, A. Millet and M. Sanz-SOLÉ, Approximation and support theorem in Hölder norm for parabolic SPDE's, Ann. Probab. 23 (1) (1995) 178-222. | MR 1330767 | Zbl 0835.60053

[3] V. Bally and E. Pardoux, Malliavin calculus for white-noise driven parabolic SPDEs, Potential Analysis, to appear. | MR 1644120 | Zbl 0928.60040

[4] N. Bouleau and F. Hirsch, Dirichlet Forms and Analysis on the Wiener Space, De Gruyter Studies in Math., Vol. 14, Walter de Gruyter, 1991. | MR 1133391 | Zbl 0748.60046

[5] J.M. Burgers, The Nonlinear Diffusion Equation, Reidel, Dordrecht, 1974. | Zbl 0302.60048

[6] G. Da Prato, A. Debussche and R. Temam, Stochastics Burgers equation, Preprint No. 27, Scuola Normale de Pisa (1995). | MR 1300149

[7] G. Da Prato and D. Gatarek, Stochastics Burgers equation, Stochastics and Stochastics Rep. 52 (1995) 29-41. | MR 1380259 | Zbl 0853.35138

[8] I. Gyongy, On the stochastic Burgers equation, Stochastic Process. Appl. 73 (1998) 271-299.

[9] E. Hopf, The partial differential equation ut + uux = μuxx, Comm. Pure Appl. Math. 3 (1950) 201-230. | MR 47234 | Zbl 0039.10403

[10] N. Lanjri Zaidi and D. Nualart, Burgers equation driven by space-time white noise: absolute continuity of the solution, Preprint (1997).

[11] M. Metivier, Semimartingales, de Gruyter, 1982. | MR 688144 | Zbl 0503.60054

[12] P.L. Morien, Hölder and Besov regularity for the density of the solution of a white-noise driven parabolic SPDE (1995), in: Bernoulli: The Official Journal of the Bernoulli Society, to appear. | MR 1681699 | Zbl 0932.60072

[13] P.L. Morien, Approximation of the density of the solution of a nonlinear SDE. Application to parabolic SPDE's, Stochastic Process. Appl. 69 (1997) 195-216. | MR 1472951 | Zbl 0911.60047

[14] D. Nualart, Malliavin Calculus and Related Fields, Springer, 1995. | MR 1344217 | Zbl 0837.60050

[15] E. Pardoux and Z. Tusheng, Absolute continuity of the law of the solution of a parabolic SPDE, J. Funct. Anal. 112 (1993) 447-458. | MR 1213146 | Zbl 0777.60046

[16] J.B. Walsh, An introduction to stochastic partial differential equations, in: Ecole d'Été de Probabilités de Saint-Flour 14, Lecture Notes in Math., Vol. 1180, Springer, 1986, pp. 265-439. | MR 876085 | Zbl 0608.60060