Large deviations from the mckean-vlasov limit for weakly interacting diffusions

References

• Bauer , H. 1981 . Probability Theory and Elements of Measure Theory , London : Adademic Press .
   Google Scholar
• Billingsley , P. 1968 . Convrgnce of Probability Measures , New York : John Wiley and sons .
   Google Scholar
• Billingsley , P. 1961 . “ Elements de mathematique, prem.part,fasc. II ” . In livre III:Topologie generale , Paris : Hermann .
   Google Scholar
• Cassandro , M. , Galves , A. , Olivieri , E. and Vares , M.E. 1984 . Metastable behavior of stochastic dynamics:A pathwise approach . J. Statist. Phys , 35 : 603 – 634 .
   Web of Science ®Google Scholar
• Comets , I. 1985 . Tunnelling and nucleation for a local mean field model Preprint
   Google Scholar
• Sanov , I. Csiszar . 1984 . property, generalized /-projection and a conditional limit theorem . Ann. Prob , 12 : 768 – 793 .
   Web of Science ®Google Scholar
• Dawson , D.A. 1983 . Critical dynamics and fluctuations for a mean field mode! of cooperative behavior . J. Statist. Phys , 31 : 29 – 85 .
   Web of Science ®Google Scholar
• Dawson , D. J. and Gärtner , J. 1984 . “ Long-time fluctuations of weakly interacting diffusions ” . In Technical Report Series of the Laboratory for Research in Statistics and Probability , Vol. 47 , Ottawa : Carleton University .
   Google Scholar
• Desai , R.C. and Zwanzig , R. 1978 . Statistical mechanics of a nonlinear stochastic model . J. Statist. Phys , 19 : 1 – 24 .
   Web of Science ®Google Scholar
• Donsker , M. D. and Varadhan , S.R.S. 1976 . Asymptotic evaluation of certain Markov process expectations for large time . III, Com. Pure Appi Math , 29 : 389 – 461 .
   Web of Science ®Google Scholar
• Dynkin , M. D. 1965 . Markov Processes , Edited by: Dynkin , E.B. Vol. 1 , Berlin : Springer-Verlag .
   Google Scholar
• Edwards , R. E. 1965 . Functional Analysis, Theory and Applications , New York : Holt, Rinehart and Winston .
   Google Scholar
• Ellis , R. S. 1985 . Entropy, Large Deviations and Statistical Mechanics , New York : Springer-Verlag .
   Google Scholar
• Ellis , R. S. and Newman , C.M. 1978 . The statistics of Curie-Weiss models . J. Statist. Phys , : 149 – 161 .
   Web of Science ®Google Scholar
• Faris , W. G. and Jona-Lasinio , G. 1982 . Large fluctuations for a nonlinear heat equation with noise . J. Phys. A:Math. Gen , 15 : 3025 – 3055 .
   Google Scholar
• Freidlin , M. I. and Wentzell , A.D. 1984 . Random Perturbations of Dynamical Systems , New York : Springer-Verlag .
   Google Scholar
• Funaki , T. 1984 . A certain class of diffusion processes associated with nonlinear parabolic equations . Z. Wahrsch. verw. Gehiete , 67 : 331 – 348 .
   Web of Science ®Google Scholar
• Gärtner , J. 1976 . On the logarithmic asymptotics of large deviation probabilities in Russian Moscow
   Google Scholar
• Gärtner , J. 1977 . On large deviations from the invariant measure . Theory Probab. Appl , 22 : 24 – 39 .
   Web of Science ®Google Scholar
• Gärtner , J. 1985 . On the McKean-Vlasov limit for interacting diffusions Preprint
   Google Scholar
• Groeneboorn , P. , Oosterhoff , J. and Ruymgaart , F.H. 1979 . Large deviation theorems for empirical probability measures . Ann. Probab , 7 : 553 – 586 .
   Web of Science ®Google Scholar
• Ikeda , N. and Watanable , S. 1981 . Stochastic Differential equations and Diffusion Processes , Amsterdam : North-Holland .
   Google Scholar
• Jacod , J. 1979 . “ Calcul stochastique et problemes de martingales, Lecture Notes in Math. 714 ” . Berlin : Springer-Verlag .
   Google Scholar
• Ladyzenskaya , O. A. , Solonnikov , V.A. and Ural'ceva , N.N. 1968 . “ Linear and quasilinear equations of parabolic type, Amer. Math. Soc. Translations of Math. Monographs ” . Providence . No.23
   Google Scholar
• Leonard , C. 1984 . “ Une loi des grands nombres pour des systemes de diffusions avec interaction et a coefficients non bornes,Technical Report Series of the Laboratory for Research in Statistics and Probability ” . Ottawa : Carleton University . No.48
   Google Scholar
• Rudin , W. 1973 . Functional Analysis , New York : McGraw-Hill .
   Google Scholar
• Ruget , G. 1982 . Grandes deviations et dynamique des populations Preprint
   Google Scholar
• Stroock , D. W. 1984 . in Introduction to the Theory of Large Deviations , New York : Springer-Verlag .
   Google Scholar
• Stroock , D. W. and Varadhan , S.R.S. 1979 . Multidimensional Diffusion Processes , Berlin : Springer-Verlag .
   Google Scholar
• Tamura , Y. 1984 . On the asymptotic behavior of the solution of a non-linear diffusion equation . J. Fac. Sci. Univ. Tokyo, Sect. I A, Math , 31 : 195 – 221 .
   Google Scholar
• Tanaka , H. 1982 . Limit theorems for certain diffusion processes with interaction, Proc. Taniguchi Int . Syp. Stoch. Anal , 31
   Google Scholar
• Varadhan , S. R. S. 1984 . “ Large deviations and applications, CBMS-NSF Regional Confrence Seres in Applied Mathematics ” . Vol. 46 , Philadelphia : SIAM .
   Google Scholar