Hilbert-valued anticipating stochastic differential equations
Annales de l'I.H.P. Probabilités et statistiques, Volume 30 (1994) no. 1, p. 133-161
@article{AIHPB_1994__30_1_133_0,
     author = {Grorud, Axel and Nualart, David and Sanz-Sol\'e, Marta},
     title = {Hilbert-valued anticipating stochastic differential equations},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {30},
     number = {1},
     year = {1994},
     pages = {133-161},
     zbl = {0796.60061},
     mrnumber = {1262894},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1994__30_1_133_0}
}
Grorud, Axel; Nualart, David; Sanz-Solé, Marta. Hilbert-valued anticipating stochastic differential equations. Annales de l'I.H.P. Probabilités et statistiques, Volume 30 (1994) no. 1, pp. 133-161. http://www.numdam.org/item/AIHPB_1994__30_1_133_0/

[1] H. Doss and G. Royer, Processus de diffusion associé aux mesures de Gibbs, Z. Wahrsch. Verw. Geb., Vol. 46, 1978, pp. 107-124. | MR 512335 | Zbl 0384.60076

[2] X. Fernique, Régularité de fonctions aléatoires non gaussiennes, École d'été de probabilités de Saint-Flour, XI-1981, P. L. HENNEQUIN Ed., Lecture Notes in Math., No. 976, Springer-Verlag, Berlin-Heidelberg-New York, 1983. | MR 722982 | Zbl 0507.60027

[3] A. Grorud and E. Pardoux, Intégrales hilbertiennes anticipantes par rapport à un processus de Wiener cylindrique et calcul stochastique associé, Applied Math. and Optimization, Vol. 25, 1992, pp. 31-49. | MR 1133251 | Zbl 0754.60051

[4] R. Holley and D. Stroock, Diffusions on an Infinite Dimensional Torus, J. Funct. Anal., Vol. 42, 1981, pp. 29-63. | MR 620579 | Zbl 0501.58039

[5] P. Imkeller, Existence and Continuity of Occupation Densities of Stochastic Integral Processes, Annals of Probability, Vol. 21, 1993, pp. 1050-1072. | MR 1217580 | Zbl 0779.60050

[6] H. Kunita, Stochastic Differential Equations and Stochastic Flow of Diffeomorphisms, École d'été de probabilités de Saint-Flour, XII-1982, P. L. HENNEQUIN Ed., Lecture Notes in Math., No. 1097, Springer-Verlag, Berlin-Heidelberg-New York, 1984. | MR 876080 | Zbl 0554.60066

[7] G. Leha and G. Ritter, On Diffusion Processes and their Semigroups in Hilbert spaces with an Application to interacting Stochastic System, Ann. Probab., Vol. 12, 1984, pp. 1077-1112. | MR 757771 | Zbl 0546.60082

[8] M. Métivier, Semimartingales, a Course on Stochastic Processes, De Gruyter Studies in Mathematics 2, Walter de Gruyter, Berlin-New York, 1982. | MR 688144 | Zbl 0503.60054

[9] A. Millet, D. Nualart and M. Sanz, Time Reversal for Infinite-Dimensional Diffusions, Probab. Th. Rel. Fields, Vol. 82, 1989, pp. 315-347. | MR 1001517 | Zbl 0659.60107

[10] A. Millet, D. Nualart and P. Sanz, Large Deviations for a Class of Anticipating Stochastic Differential Equations, Annals of Probability, Vol. 20, 1992, pp. 1902-1931. | MR 1188048 | Zbl 0769.60053

[11] D. Nualart and M. Zakai, Generalized Stochastic Integrals and the Malliavin Calculus, Prob. Th. Rel. Fields, Vol. 73, 1986, pp. 255-280. | MR 855226 | Zbl 0601.60053

[12] D. Nualart and E. Pardoux, Stochastic Calculus with Anticipating Integrands, Prob. Th. Rel. Fields, Vol. 78, 1988, pp. 535-581. | MR 950346 | Zbl 0629.60061

[13] D. Ocone and E. Pardoux, A Generalized Itô-Ventzell Formula. Applications to a Class of Anticipating Stochastic Differential Equations, Ann. Inst. Henri Poincaré, Vol. 25, 1989, pp. 39-71. | Numdam | MR 995291 | Zbl 0674.60057

[14] B. Rozovski, Stochastic Evolutions Systems, Kluwer Academic Publishers, 1990. | MR 1135324

[15] T. Shiga, A. Shimizu, Infinite Dimensional Stochastic Differential Equations and their Applications, J. Math. Kyoto Univ., Vol. 20, 1980, pp. 395-416. | MR 591802 | Zbl 0462.60061

[16] M. Talagrand, Sample Boundedness of Stochastic Processes Under Increment Conditions, Ann. Probab., Vol. 18, 1990, pp. 1-49. | MR 1043935 | Zbl 0703.60033

[17] M. Yor, Existence et unicité de diffusions à valeurs dans un espace de Hilbert, Ann. Inst. Henri Poincaré, Vol. X, 1974, pp. 55-88. | Numdam | MR 356257 | Zbl 0281.60094