Propagation of chaos and fluctuations for a moderate model with smooth initial data

Annales de l'institut Henri Poincare (B) Probability and Statistics

Volumn 34, Issue 6, 1998, Pages 727-766

  Jourdain, B ^a   Meleard S ^b,c  

^a UNIVERSITÉ PARIS EST   (France)

^b University of Paris VII LPSM partially supported by ERC Starting Grant 680275 MALIG   (France)

^c UNIVERSITÉ PARIS OUEST NANTERRE LA DÉFENSE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032325532     PISSN: 02460203     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0246-0203(99)80002-8     Document Type: Article

References (16)

1. [1] R.A. ADAMS, Sobolev Spaces, Academic Press, 1978.
2. [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.
3. [3] A. FRIEDMAN, Stochastic Differential Equations and Applications, volume 1, Academic Press, 1975.
4. [4] I.I. GIHMAN and A.V. SKOROHOD, Stochastic differential equations, Springer-Verlag, 1972.
5. [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.
6. [6] O.A. LADYZENSKAYA, V.A. SOLONNIKOV, and N.N. URAL'CEVA , Linear and Quasilinear Equations of Parabolic Type, volume 23 of Translations of Mathematical Monographs. American Mathematical Society, 1968.
7. [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.
8. [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.
9. [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.
10. [10] P.A. MEYER, Probabilités et Potentiel, Hermann, 1966.
11. [11] I. MITOMA, An ∞-dimensional inhomogeneous langevin's equation, Journal of Functional Analysis, 61:, 1985, pp. 342-359.
12. [12] D. NUALART, The Malliavin Calculus and Related Topics. Springer-Verlag, 1995.
13. [13] K. OELSCHLÄGER, A law of large numbers for moderately interacting diffusion processes, Z. Wahrsch. Verw. Geb., 69, 1985, pp. 279-322.
14. [14] K. OELSCHLÄGER, A fluctuation theorem for moderately interacting diffusion processes. Probab. Th. Rel. Fields, 74, 1987, pp. 591-616.
15. [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.
16. [16] K. YOSIDA, Functional Analysis, Springer-Verlag, sixth edition, 1980.