Stochastic heat equation with white-noise drift
Annales de l'I.H.P. Probabilités et statistiques, Volume 36 (2000) no. 2, p. 181-218
@article{AIHPB_2000__36_2_181_0,
     author = {Al\`os, Elisa and Nualart, David and Viens, F.},
     title = {Stochastic heat equation with white-noise drift},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {36},
     number = {2},
     year = {2000},
     pages = {181-218},
     zbl = {0970.60068},
     mrnumber = {1751658},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2000__36_2_181_0}
}
Alòs, E.; Nualart, D.; Viens, F. Stochastic heat equation with white-noise drift. Annales de l'I.H.P. Probabilités et statistiques, Volume 36 (2000) no. 2, pp. 181-218. http://www.numdam.org/item/AIHPB_2000__36_2_181_0/

[1] Alòs E., León J.A., Nualart D., Stochastic heat equation with random coefficients, Probab. Theory Related Fields 115 (1999) 41-94. | MR 1715545 | Zbl 0939.60065

[2] Alòs E., Nualart D., An extension of Itô's formula for anticipating processes, J. Theoretical Probab. 11 (1998) 493-514. | MR 1622583 | Zbl 0914.60018

[3] Da Prato G., Zabczyk J., Stochastic Equations in Infinite Dimensions, Cambridge University Press, 1992. | MR 1207136 | Zbl 0761.60052

[4] Friedman A., Partial Differential Equations of Parabolic Type, Prentice-Hall, 1964. | MR 181836 | Zbl 0144.34903

[5] Hu Y., Nualart D., Continuity of some anticipating integral processes, Statist. Probab. Lett. 37 (1998) 203-211. | MR 1620482 | Zbl 0894.60044

[6] Kifer Y., Kunita H., Random positive semigroups and their random infinitesimal generators, in: Davies I.M., Truman A., Elworthy K.D. (Eds.), Stochastic Analysis and Applications, World Scientific, 1996, pp. 270-285. | MR 1453138 | Zbl 0935.60043

[7] Kunita H., Stochastic Flows and Stochastic Differential Equations, Cambridge University Press, 1990. | MR 1070361 | Zbl 0743.60052

[8] Kunita H., Generalized solutions of a stochastic partial differential equation, J. Theoretical Probab. 7 (1994) 279-308. | MR 1270604 | Zbl 0802.60056

[9] León J.A., Nualart D., Stochastic evolution equations with random generators, Ann. Probab. 26 (1998) 149-186. | MR 1617045 | Zbl 0939.60066

[10] Malliavin P., Stochastic calculus of variations and hypoelliptic operators, in: Proc. Inter. Symp. on Stoch. Diff. Eq., Kyoto, 1976, Wiley, 1978, pp. 195-263. | Zbl 0411.60060

[11] Nualart D., The Malliavin Calculus and Related Topics, Springer-Verlag, 1995. | MR 1344217 | Zbl 0837.60050

[12] Nualart D., Pardoux E., Stochastic calculus with anticipating integrands, Probab. Theory Related Fields 78 (1988) 535-581. | MR 950346 | Zbl 0629.60061

[13] Nualart D., Viens F., Evolution equation of a stochastic semigroup with white-noise drift, Ann. Probab., to appear. | MR 1755997 | Zbl 1044.60052

[14] Pardoux E., Protter Ph., Two-sided stochastic integrals and calculus, Probab. Theory Related Fields 76 (1987) 15-50. | MR 899443 | Zbl 0608.60058

[15] Skorohod A.V., On a generalization of a stochastic integral, Theory Probab. Appl. 20 (1975) 219-233. | MR 391258 | Zbl 0333.60060

[16] Walsh J.B., An introduction to stochastic partial differential equations, in: Lecture Notes in Mathematics, Vol. 1180, Springer, Berlin, 1984, pp. 264-437. | MR 876085 | Zbl 0608.60060

[17] Zakai M., Some moment inequalities for stochastic integrals and for solutions of stochastic differential equations, Israel J. Math. 5 (1967) 170-176. | MR 225397 | Zbl 0166.13803