McKean-Vlasov limit for interacting random processes in random media

Journal of Statistical Physics

Volumn 84, Issue 3-4, 1996, Pages 735-772

  Dai Pra, Paolo ^a   Den Hollander, Frank ^b  

^a UNIVERSITY OF PADOVA   (Italy)

^b RADBOUD UNIVERSITY NIJMEGEN   (Netherlands)

Author keywords

Central limit theorem; Interacting particle systems; Large deviations; McKean Vlasov equation; Random media

Indexed keywords

EID: 0030210666     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf02179656     Document Type: Article

References (17)

1. G. Ben Arous and M. Brimaud, Méthode de Laplace: Etude variationnelle des fluctuations de diffusions de type "champs moyens," Stoch. Stock. Rep. 31:79-144 (1990).
2. E. Bolthausen, Laplace approximations for sums of independent random vectors, Prob. Theory Related Fields 72:305-318 (1986).
3. H. Brezis, Analyse Fonctionnelle: Théorie et Applications (Masson, Paris, 1983).
4. M. Brunaud, Finite Kullback information diffusion laws with fixed marginals and associated large deviations functionals, Stoch. Proc. Appl. 44:329-345 (1993).
5. F. Comets, Nucleation for a long range magnetic model, Ann. Inst. H. Poincaré 23: 135-178 (1987).
6. F. Comets and Th. Eisele, Asymptotic dynamics, non-critical and critical fluctuations for a geometric long-range interacting model, Commun. Math. Phys. 118:531-567 (1988).
7. D. A. Dawson, Critical dynamics and fluctuations for a mean field model of cooperative behavior, J. Stat. Phys. 31:29-83 (1982).
8. D. A. Dawson and J. Gärtner, Large deviations from the McKean-Vlasov limit for weakly interacting diffusions, Stochastics 20:247-308 (1987).
9. J.-D. Deuschel and D. W. Stroock, Large Deviations (Academic Press, Boston, 1989).
10. S. N. Ethier and T. G. Kurtz, Markov Processes, Characterization und Convergence (Wiley, New York, 1986).
11. S. Feng, Large deviations for empirical process of mean-field interacting particle systems with unbounded jumps, Ann. Prob. 22:2122-2151 (1994).
12. H. Föllmer, Random fields and diffusion processes, in École d'Eté de Probabilités de Saint Flour XV-XVII (Springer, Berlin, 1988), pp. 101-204.
13. I. Karatzas and S. Shreve, Brownian Motion and Stochastic Calculus (Springer, New York, 1988).
14. S. Kusuoka and Y. Tamura, Gibbs measure for mean field potentials, J. Fac. Sci. Univ. Tokyo I.A 31:223-245 (1984).
15. R. S. Lipster and A. N. Shiryaev, Statistics of Random Processes, Vol. 2 (Springer, New York, 1988).
16. A.-S. Sznitman, Nonlinear reflecting diffusion process, and the propagation of chaos and fluctuations associated, J. Funct. Anal. 56:311-336 (1984).
17. S. R. S. Varadhan, Large Deviations and Applications (Society for Industrial and Applied Mathematics, Philadelphia, 1984).