Propagation of chaos and fluctuations for a moderate model with smooth initial data
Annales de l'I.H.P. Probabilités et statistiques (1998)
- Volume: 34, Issue: 6, page 727-766
- ISSN: 0246-0203
Access Full Article
topHow to cite
topJourdain, B., and Méléard, S.. "Propagation of chaos and fluctuations for a moderate model with smooth initial data." Annales de l'I.H.P. Probabilités et statistiques 34.6 (1998): 727-766. <http://eudml.org/doc/77619>.
@article{Jourdain1998,
author = {Jourdain, B., Méléard, S.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {interacting diffusion processes; trajectorial propagation of chaos; fluctuations; convergence rate},
language = {eng},
number = {6},
pages = {727-766},
publisher = {Gauthier-Villars},
title = {Propagation of chaos and fluctuations for a moderate model with smooth initial data},
url = {http://eudml.org/doc/77619},
volume = {34},
year = {1998},
}
TY - JOUR
AU - Jourdain, B.
AU - Méléard, S.
TI - Propagation of chaos and fluctuations for a moderate model with smooth initial data
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1998
PB - Gauthier-Villars
VL - 34
IS - 6
SP - 727
EP - 766
LA - eng
KW - interacting diffusion processes; trajectorial propagation of chaos; fluctuations; convergence rate
UR - http://eudml.org/doc/77619
ER -
References
top- [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. Zbl0939.60048MR1480638
- [3] A. Friedman, Stochastic Differential Equations and Applications, volume 1, Academic Press, 1975. Zbl0323.60056MR494490
- [4] I.I. Gihman and A.V. Skorohod, Stochastic differential equations, Springer-Verlag, 1972. Zbl0242.60003MR346904
- [5] H. Kunita, Stochastic differential equations and stochastic flow of diffeomorphisms, In Ecole d'été de probabilités de Saint-FlourXII - 1982, Lect. Notes in Math. 1097. Springer-Verlag, 1984. Zbl0554.60066MR876080
- [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. Zbl0174.15403
- [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. Zbl0597.60053MR850759
- [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. MR233437
- [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. Zbl0633.60108MR923112
- [10] P.A. Meyer, Probabilités et Potentiel, Hermann, 1966. Zbl0138.10402MR205287
- [11] I. Mitoma, An ∞-dimensional inhomogeneous langevin's equation, Journal of Functional Analysis, 61:, 1985, pp. 342-359. Zbl0579.60053MR820620
- [12] D. Nualart, The Malliavin Calculus and Related Topics. Springer-Verlag, 1995. Zbl0837.60050MR1344217
- [13] K. Oelschläger, A law of large numbers for moderately interacting diffusion processes, Z. Wahrsch. Verw. Geb., 69, 1985, pp. 279-322. Zbl0549.60071MR779460
- [14] K. Oelschläger, A fluctuation theorem for moderately interacting diffusion processes, Probab. Th. Rel. Fields, 74, 1987, pp. 591-616. Zbl0592.60064MR876258
- [15] A.S. Sznitman, Topics in propagation of chaos, In Ecole d'été de probabilités de Saint-FlourXIX - 1989, Lect. Notes in Math. 1464. Springer-Verlag, 1991. Zbl0732.60114MR1108185
- [16] K. Yosida, Functional Analysis, Springer-Verlag, sixth edition, 1980. MR617913
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.