@article{AIHPB_1998__34_6_727_0, author = {Jourdain, Benjamin and M\'el\'eard, S.}, title = {Propagation of chaos and fluctuations for a moderate model with smooth initial data}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, volume = {34}, year = {1998}, pages = {727-766}, mrnumber = {1653393}, zbl = {0921.60053}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPB_1998__34_6_727_0} }
Jourdain, B.; Méléard, S. Propagation of chaos and fluctuations for a moderate model with smooth initial data. Annales de l'I.H.P. Probabilités et statistiques, Tome 34 (1998) pp. 727-766. http://gdmltest.u-ga.fr/item/AIHPB_1998__34_6_727_0/
[1] Sobolev Spaces, Academic Press, 1978.
,[2] A hilbertian approach for fluctuations on the Mckean-Vlasov model, Stochastic Processes and their Applications, 71, 1997 pp. 33-53. | MR 1480638 | Zbl 0939.60048
and ,[3] Stochastic Differential Equations and Applications, volume 1, Academic Press, 1975. | MR 494490 | Zbl 0323.60056
,[4] Stochastic differential equations, Springer-Verlag, 1972. | MR 346904 | Zbl 0242.60003
and ,[5] Stochastic differential equations and stochastic flow of diffeomorphisms, In Ecole d'été de probabilités de Saint-Flour XII - 1982, Lect. Notes in Math. 1097. Springer-Verlag, 1984. | MR 876080 | Zbl 0554.60066
,[6] Linear and Quasilinear Equations of Parabolic Type, volume 23 of Translations of Mathenzatical Monographs. American Mathematical Society, 1968. | Zbl 0174.15403
, , and ,[7] Une loi des grands nombres pour des systèmes de diffusions avec interaction et à coefficients non bornés, Ann. Inst. Henri Poincaré, 22(2), 1986, pp. 237-262. | Numdam | MR 850759 | Zbl 0597.60053
,[8] Propagation of chaos for a class of non-linear parabolic equations, In Lecture Series in Differential Equations, 7, 1967, pp. 41-57. | MR 233437
,[9] A propagation of chaos result for a system of particles with moderate interaction, Stochastic Processes and their Applications, 26, 1987, pp. 317-332. | MR 923112 | Zbl 0633.60108
and ,[10] Probabilités et Potentiel, Hermann, 1966. | MR 205287 | Zbl 0138.10402
,[11] An ∞-dimensional inhomogeneous langevin's equation, Journal of Functional Analysis, 61:, 1985, pp. 342-359. | MR 820620 | Zbl 0579.60053
,[12] The Malliavin Calculus and Related Topics. Springer-Verlag, 1995. | MR 1344217 | Zbl 0837.60050
,[13] A law of large numbers for moderately interacting diffusion processes, Z. Wahrsch. Verw. Geb., 69, 1985, pp. 279-322. | MR 779460 | Zbl 0549.60071
,[14] A fluctuation theorem for moderately interacting diffusion processes, Probab. Th. Rel. Fields, 74, 1987, pp. 591-616. | MR 876258 | Zbl 0592.60064
,[15] Topics in propagation of chaos, In Ecole d'été de probabilités de Saint-Flour XIX - 1989, Lect. Notes in Math. 1464. Springer-Verlag, 1991. | MR 1108185 | Zbl 0732.60114
,[16] | MR 617913
, Functional Analysis, Springer-Verlag, sixth edition, 1980.