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Large deviations for Markov processes with mean field interaction and unbounded jumps


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.

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  1. [1]

    Billingsley, P.: Convergence of Probability Measures. New York: John Wiley and Sons 1968

    Google Scholar 

  2. [2]

    Chen, M.F.: Jump Processes and Particle System. Beijing: Beijing Normal University Publishing House 1986 (in Chinese)

    Google Scholar 

  3. [3]

    Comets, F.: Nucleation for a long range magnetic model. Ann. Inst. Henri Poincaré23, 137–178 (1987)

    Google Scholar 

  4. [4]

    Dawson, D.A., Gärtner, J.: Large deviations from the Mckean-Vlasov limit for weakly interacting diffusions. Stochastics20, 247–308 (1987)

    Google Scholar 

  5. [5]

    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)

    Google Scholar 

  6. [6]

    Ethier, S.N., Kurtz, T.G.: Markov Processes: Characterization and Convergence. New York: Wiley 1986

    Google Scholar 

  7. [7]

    Feng, S., Zheng, X.: Solutions of a class of nonlinear master equations. Stochastic Processes Appl.43, 65–84 (1992)

    Google Scholar 

  8. [8]

    Feng, S.: Large deviations for the empirical processes of mean field particle system with unbounded jumps. Ann Probab. (to appear 1993)

  9. [9]

    Freidlin, M.I., Wentzell, A.D.: Random Perturbations of Dynamical Systems. Berlin Heidelberg New York: Springer 1984

    Google Scholar 

  10. [10]

    Gärtner, J.: On the Mckean-Vlasov limit for interacting diffusions. Math. Nachr.137, 197–248 (1988)

    Google Scholar 

  11. [11]

    Ikeda, N., Watanabe, S.: Stochastic Differential Equations and Diffusion Processes. Amsterdam: North-Holland Publishing Company 1981

    Google Scholar 

  12. [12]

    Léonard, C.: Large deviations in the dual of a normed vector space. Prépublication de I'Université d'Orsay, 1990

  13. [13]

    Léonard, C.: On large deviations for particle systems associated with spatially homogeneous Boltzmann type equations. (Preprint 1990)

  14. [14]

    Nicolis, G., Prigogine, I.: Self-organization in Non-equilibrium Systems. New York: Wiley 1977

    Google Scholar 

  15. [15]

    Schlögl, F.: Chemical reaction models for non-equilibrium phase transitions. Z. Phys.253, 147–161 (1972)

    Google Scholar 

  16. [16]

    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)

    Google Scholar 

  17. [17]

    Stroock, D.W., Varadhan, S.R.S.: Multidimensional Diffusion Processes, Berlin Heidelberg New York: Springer 1979

    Google Scholar 

  18. [18]

    Stroock, D.W.: An Introduction to the Theory of Large Deviations Berlin Heidelberg New York: Springer 1984

    Google Scholar 

  19. [19]

    Sugiura, M.: Large deviations for Markov processes of jump type with mean-field interactions. (Preprint 1990)

Download references

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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

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Feng, S. Large deviations for Markov processes with mean field interaction and unbounded jumps. Probab. Th. Rel. Fields 100, 227–252 (1994).

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Mathematics Subject Classifications (1991)

  • 60F10
  • 60J75
  • 60K35
  • 82C26