no. 2
Large deviations for long range interacting particle systems with jumps
Annales de l'I.H.P. Probabilités et statistiques, Tome 31 (1995) no. 2, pp. 289-323. 
@article{AIHPB_1995__31_2_289_0,
     author = {L\'eonard, Christian},
     title = {Large deviations for long range interacting particle systems with jumps},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {289--323},
     publisher = {Gauthier-Villars},
     volume = {31},
     number = {2},
     year = {1995},
     mrnumber = {1324810},
     zbl = {0839.60032},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1995__31_2_289_0/}
}
TY  - JOUR
AU  - Léonard, Christian
TI  - Large deviations for long range interacting particle systems with jumps
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 1995
SP  - 289
EP  - 323
VL  - 31
IS  - 2
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPB_1995__31_2_289_0/
LA  - en
ID  - AIHPB_1995__31_2_289_0
ER  - 
%0 Journal Article
%A Léonard, Christian
%T Large deviations for long range interacting particle systems with jumps
%J Annales de l'I.H.P. Probabilités et statistiques
%D 1995
%P 289-323
%V 31
%N 2
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPB_1995__31_2_289_0/
%G en
%F AIHPB_1995__31_2_289_0
Léonard, Christian. Large deviations for long range interacting particle systems with jumps. Annales de l'I.H.P. Probabilités et statistiques, Tome 31 (1995) no. 2, pp. 289-323. http://www.numdam.org/item/AIHPB_1995__31_2_289_0/

[BAB] G. Ben Arous and M. Brunaud, Méthode de Laplace. Étude variationnelle des fluctuations de diffusions de type « champ moyen », Stochastics and Stoch. Rep., Vol. 31, 1990, pp. 79-144. | MR | Zbl

[Bil] P. Billingsley, Convergence of probability measures, J. Wiley and Sons, New York, 1968. | MR | Zbl

[Bru] M. Brunaud, Finite Kullback information diffusion laws with fixed marginals and associated large deviations functionals, Stoch. Proc. and Appl., Vol. 44, 1993, pp. 329-345. | MR | Zbl

[CaL] P. Cattiaux and C. Léonard, Minimization of the Kullback information of diffusion processes, Ann. Inst. Henri Poincaré, Vol. 30, 1994, pp. 83-132. | Numdam | MR | Zbl

[Com] F. Comets, Nucleation for a longe range magnetic model, Ann. Inst. Henri Poincaré, Vol. 23, No. 2, 1987, pp. 137-178. | Numdam | MR | Zbl

[Daw] D.A. Dawson, Critical dynamics and fluctuations for a mean-field model of cooperative behavior, Journal of Statistical Physics, t. 31, No. 1, 1983, pp. 29-85. | MR

[DeS] J.D. Deuschel and D.W. Stroock, Large Deviations, Pure and Applied Mathematics, Vol. 137, 1987, Academic Press, Boston. | MR | Zbl

[DaG] D.A. Dawson and J. Gärtner, Large deviations from the McKean-Vlasov limit for weakly interacting diffusions, Stochastics and Stoch. Rep., Vol. 20, 1987, pp. 247-308. | MR | Zbl

[DZe] A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications, Jones and Bartlett Publishers, 1993. | MR | Zbl

[EiE] T. Eisele and R.S. Ellis, Symmetry breaking and random waves for magnetic sytems on a circle, Z. Wahrsch. verw. Geb., Vol. 63, 1978, p. 297. | MR | Zbl

[Fen] S. Feng, Large deviations for empirical process of mean field interacting particle system with unbounded jumps, to appear in Ann. Probab. | MR | Zbl

[Fö1] H. Föllmer, An entropy approach to the time reversal of diffusion processes. Proc. 4th IFIP Workshop on Stochastic Differential Equations, 1985, M. MÉTIVIER and E. PARDOUX, Eds., Lecture Notes in Control and Information Sciences, Springer Verlag. | MR | Zbl

[Fö2] H. Föllmer, Random Fields and Diffusion Processes. Cours à l'École d'été de Probabilités de Saint-Flour, 1988, Lecture Notes in Mathematics, Vol. 1362, Springer Verlag. | MR | Zbl

[Gär] J. Gärtner, On the McKean-Vlasov limit for interacting diffusions, Math. Nach., Vol. 137, 1988, pp. 197-248. | MR | Zbl

[Jac] J. Jacod, Calcul stochastique et problèmes de martingales. Lecture Notes in Mathematics, Vol. 714, 1979, Springer-Verlag. | MR | Zbl

[KRu] M.A. Krasnosel'Skii and Ya.B. Rutickii, Convex functions and Orlicz spaces, 1961, P. Noordhoff Ltd. | MR | Zbl

[Lé1] C. Léonard, Une loi des grands nombres pour des systèmes de diffusion avec interaction et à coefficients non bornés, Ann. Inst. Henri Poincaré, Vol. 22, No. 2, 1986, pp. 237-262. | Numdam | MR | Zbl

[Lé2] C. Léonard, Some epidemic systems are long range interacting particle systems, in Stochastic Processes in Epidemic Theory, 1990, Lecture Notes in Biomathematics, Vol. 86. | Zbl

[Lé3] C. Léonard, Large deviations for particle systems associated with spatially homogeneous Boltzmann type equations, Prob. Th. Rel. Fields, Vol. 101, No. 1, 1995, pp. 1-44. | MR | Zbl

[McK] H.P. Mckean, Propagation of chaos for a class of nonlinear parabolic equations. Catholic University (Washington D. C.), Lecture Series in Differential Equations, 1967.

[Nev] J. Neveu, Martingales à temps discret, Masson, 1972. | MR

[Oel] K. Oelschläger, A martingale approach to the law of large numbers for weakly interacting stochastic processes, Ann. Probab., Vol. 12, No. 2, 1984, pp. 458-479. | MR | Zbl

[Rac] S.T. Rachev, Probability metrics and the stability of stochastic models, J. Wiley, New York, 1991. | MR | Zbl

[ShT] T. Shiga and H. Tanaka, Central limit theorem for a system of Markovian particles with mean field interactions. Z. Wahrsch. verw. Geb., Vol. 69, 1985, pp. 439-459. | MR | Zbl

[Sug] M. Sugiura, Large deviations for Markov process of jump type with mean field interactions, Preprint, 1990.

[Sz1] A.S. Sznitman, Nonlinear reflecting diffusion process, the propagation of chaos and fluctuations associated, J. Funct. Anal., Vol. 56, 1984, pp. 311-336. | MR | Zbl

[Sz2] A.S. Sznitman, Equations de type Boltzmann, spatialement homogènes, Z. Wahrsch. verw. Geb., Vol. 66, 1984, pp. 559-592. | MR | Zbl

[Sz3] A.S. Sznitman, Cours à l'école d'été de probabilités de Saint-Flour, 1989, Lecture Notes in Mathematics, Vol. 1464, 1991. | Zbl

[Tan] H. Tanaka, Limit theorems for certain diffusion processes with interaction, Proc. Tanigushi Int. Symp. of Stoch. Anal., 1982. | Zbl

[Var] S.R.S. Varadhan, Asymptotic Probabilities and Differential Equations, Comm. Pure Appl. Math., Vol. 1, 1966, pp. 261-286. | MR | Zbl