Summary
An N-particle system with mean field interaction is considered. The large deviation estimates for the empirical distributions as N goes to infinity are obtained under conditions which are satisfied, by many interesting models including the first and the second Schlögl models.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Billingsley, P.: Convergence of Probability Measures. New York: John Wiley and Sons 1968
Chen, M.F.: Jump Processes and Particle System. Beijing: Beijing Normal University Publishing House 1986 (in Chinese)
Comets, F.: Nucleation for a long range magnetic model. Ann. Inst. Henri Poincaré23, 137–178 (1987)
Dawson, D.A., Gärtner, J.: Large deviations from the Mckean-Vlasov limit for weakly interacting diffusions. Stochastics20, 247–308 (1987)
Dawson, D.A., Zheng, X.: Law of large numbers and a central limit theorem for unbounded jump mean-field models. Adv. Appl. Math.12, 293–326 (1991)
Ethier, S.N., Kurtz, T.G.: Markov Processes: Characterization and Convergence. New York: Wiley 1986
Feng, S., Zheng, X.: Solutions of a class of nonlinear master equations. Stochastic Processes Appl.43, 65–84 (1992)
Feng, S.: Large deviations for the empirical processes of mean field particle system with unbounded jumps. Ann Probab. (to appear 1993)
Freidlin, M.I., Wentzell, A.D.: Random Perturbations of Dynamical Systems. Berlin Heidelberg New York: Springer 1984
Gärtner, J.: On the Mckean-Vlasov limit for interacting diffusions. Math. Nachr.137, 197–248 (1988)
Ikeda, N., Watanabe, S.: Stochastic Differential Equations and Diffusion Processes. Amsterdam: North-Holland Publishing Company 1981
Léonard, C.: Large deviations in the dual of a normed vector space. Prépublication de I'Université d'Orsay, 1990
Léonard, C.: On large deviations for particle systems associated with spatially homogeneous Boltzmann type equations. (Preprint 1990)
Nicolis, G., Prigogine, I.: Self-organization in Non-equilibrium Systems. New York: Wiley 1977
Schlögl, F.: Chemical reaction models for non-equilibrium phase transitions. Z. Phys.253, 147–161 (1972)
Shiga, T., Tanaka, H.: Central limit theorem for a system of Markovian particles with mean-field interactions. Z. für. Wahrscheinlichkeitstheor Verw. Geb.69, 439–459 (1985)
Stroock, D.W., Varadhan, S.R.S.: Multidimensional Diffusion Processes, Berlin Heidelberg New York: Springer 1979
Stroock, D.W.: An Introduction to the Theory of Large Deviations Berlin Heidelberg New York: Springer 1984
Sugiura, M.: Large deviations for Markov processes of jump type with mean-field interactions. (Preprint 1990)
Author information
Authors and Affiliations
Additional information
Supported partially by a scholarship from the Faculty of Graduate Studies and Research of Carleton University and the NSERC operating grant of D.A. Dawson
Rights and permissions
About this article
Cite this article
Feng, S. Large deviations for Markov processes with mean field interaction and unbounded jumps. Probab. Th. Rel. Fields 100, 227–252 (1994). https://doi.org/10.1007/BF01199267
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01199267