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) no. 6, pp. 727-766. 
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     author = {Jourdain, B. 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},
     pages = {727--766},
     publisher = {Gauthier-Villars},
     volume = {34},
     number = {6},
     year = {1998},
     mrnumber = {1653393},
     zbl = {0921.60053},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1998__34_6_727_0/}
}
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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) no. 6, pp. 727-766. http://www.numdam.org/item/AIHPB_1998__34_6_727_0/

[1] R.A. Adams, Sobolev Spaces, Academic Press, 1978.

[2] B. Fernandez and S. Méléard, A hilbertian approach for fluctuations on the Mckean-Vlasov model, Stochastic Processes and their Applications, 71, 1997 pp. 33-53. | MR | Zbl

[3] A. Friedman, Stochastic Differential Equations and Applications, volume 1, Academic Press, 1975. | MR | Zbl

[4] I.I. Gihman and A.V. Skorohod, Stochastic differential equations, Springer-Verlag, 1972. | MR | Zbl

[5] H. Kunita, 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 | Zbl

[6] O.A. Ladyzenskaya, V.A. Solonnikov, and N.N. Ural'Ceva , Linear and Quasilinear Equations of Parabolic Type, volume 23 of Translations of Mathenzatical Monographs. American Mathematical Society, 1968. | Zbl

[7] C. Léonard, 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. | EuDML | Numdam | MR | Zbl

[8] H.P. Mckean, Propagation of chaos for a class of non-linear parabolic equations, In Lecture Series in Differential Equations, 7, 1967, pp. 41-57. | MR

[9] S. Méléard and S. Roelly-Coppoletta, A propagation of chaos result for a system of particles with moderate interaction, Stochastic Processes and their Applications, 26, 1987, pp. 317-332. | MR | Zbl

[10] P.A. Meyer, Probabilités et Potentiel, Hermann, 1966. | MR | Zbl

[11] I. Mitoma, An ∞-dimensional inhomogeneous langevin's equation, Journal of Functional Analysis, 61:, 1985, pp. 342-359. | MR | Zbl

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

[13] K. Oelschläger, A law of large numbers for moderately interacting diffusion processes, Z. Wahrsch. Verw. Geb., 69, 1985, pp. 279-322. | MR | Zbl

[14] K. Oelschläger, A fluctuation theorem for moderately interacting diffusion processes, Probab. Th. Rel. Fields, 74, 1987, pp. 591-616. | MR | Zbl

[15] A.S. Sznitman, 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 | Zbl

[16] K. Yosida, Functional Analysis, Springer-Verlag, sixth edition, 1980. | MR