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Ferland, René; Fernique, Xavier; Giroux, Gaston. Compactness of the Fluctuations Associated with some Generalized Nonlinear Boltzmann Equations. Canadian journal of mathematics, Tome 44 (1992) no. 6, pp. 1192-1205. doi: 10.4153/CJM-1992-071-1
@article{10_4153_CJM_1992_071_1,
author = {Ferland, Ren\'e and Fernique, Xavier and Giroux, Gaston},
title = {Compactness of the {Fluctuations} {Associated} with some {Generalized} {Nonlinear} {Boltzmann} {Equations}},
journal = {Canadian journal of mathematics},
pages = {1192--1205},
year = {1992},
volume = {44},
number = {6},
doi = {10.4153/CJM-1992-071-1},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1992-071-1/}
}
TY - JOUR AU - Ferland, René AU - Fernique, Xavier AU - Giroux, Gaston TI - Compactness of the Fluctuations Associated with some Generalized Nonlinear Boltzmann Equations JO - Canadian journal of mathematics PY - 1992 SP - 1192 EP - 1205 VL - 44 IS - 6 UR - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1992-071-1/ DO - 10.4153/CJM-1992-071-1 ID - 10_4153_CJM_1992_071_1 ER -
%0 Journal Article %A Ferland, René %A Fernique, Xavier %A Giroux, Gaston %T Compactness of the Fluctuations Associated with some Generalized Nonlinear Boltzmann Equations %J Canadian journal of mathematics %D 1992 %P 1192-1205 %V 44 %N 6 %U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1992-071-1/ %R 10.4153/CJM-1992-071-1 %F 10_4153_CJM_1992_071_1
[1] 1. Barnsley, M.F. and Turchetti, G., A Study of Boltzmann Energy Equations, Ann. Phys. 159(1985), 1–61. Google Scholar
[2] 2. Barrachina, R.O., Wild's Solution of the Nonlinear Boltzmann Equation, J. Statist. Phys. 52( 1988), 357–368. Google Scholar
[3] 3. Billingsley, P., Convergence of Probability Measures, Wiley, New York, 1968. Google Scholar
[4] 4. Bojdeckiand, T. Gorostiza, L.G., Langevin equationsfor S’ -valued gaussian processes andfluctuation limits of infinite particle systems, Probab. Th. Rel. Fields 73(1986), 227–244. Google Scholar
[5] 5. Dawson, D.A., Critical dynamics and fluctuations for a mean field model of cooperative behaviour, J. Statist. Phys. 31(1983), 29–85. Google Scholar
[6] 6. Ethier, S.N. and Kurtz, T.G., Markov Processes. Characterization and convergence, Wiley, New York, 1986. Google Scholar
[7] 7. Ferland, R., Equations de Boltzmann scalaires : convergence de la solution, fluctuations et propagation du chaos trajectorielle, Thèse de doctorat, Université de Sherbrooke, 1990. Google Scholar
[8] 8. Ferland, R., Éluctuations pour des équations de Boltzmann scalaires, Can. J. Math. 43(1991), 975–984. Google Scholar
[9] 9. Fernique, X., Convergence en loi de fonctions aléatoires continues ou cadlag, propriétés de compacité des lois, Rapport CRM-1716, Centre de recherches mathématiques, Université de Montréal, 1990. Google Scholar
[10] 10. Futcher, F.J., Hoare, M.R., Hendriks, E.M. and Ernst, M.H., Soluble Boltzmann equations for internal state and Maxwell models, Phys. (A) 101(1980), 185–204. Google Scholar
[11] 11. Futcher, F.J. and Hoare, M.R., The p-q Model Boltzmann Equation, Phys. (A) 122( 1983), 516–546. Google Scholar
[12] 12. Gartner, J., On the McKean-Vlasov limit for interacting diffusions, Math. Nachr. 137(1988), 197–248. Google Scholar
[13] 13. Holley, R.A. andStroock, D.V., Generalized Ornstein-Uhlenbeck Processes and Infinite Particle Branching Brownian Motion, Publ. Res. Inst. Math. Sci. 14(1978), 741–788. Google Scholar
[14] 14. Hoare, M.H., Quadratic Transport and Soluble Boltzmann Equation, Adv. Chem. Phys. 56(1984), 1–140. Google Scholar
[15] 15. Kac, M., Foundations of kinetic theory, Proc. Third Berkeley Symp. Math. Statist. Prob. (ed. Neyman, J.) 3(1956), 171–197. Google Scholar
[16] 16. Kallianpur, G. and Perez, V.- Abreu, Stochastic Evolution Equations Driven by Nuclear-Space-Valued Martingales, Appl. Math. Optim. 17(1988), 237–272. Google Scholar
[17] 17. McKean, H.P., An Exponential Formula for Solving Boltzmann's Equation for a Maxwellian Gas, J. Cornbin. Theory 2(1967), 358–382. Google Scholar
[18] 18. McKean, H.P., Fluctuations in the kinetic theory of gases, Comm. Pure Appl. Math. 28(1975), 435–455. Google Scholar
[19] 19. Oelschlager, K., Limit theorems for age-structured populations, Ann. Probab. 18(1990), 290–318. Google Scholar
[20] 20. Parthasarathy, K.R., Probability measures on metric spaces Academic Press, New York, 1969. Google Scholar
[21] 21. Shiga, T. and Tanaka, H., Central limit theorem for a system of Markov ian particles with meanfield interactions, Z. Wahrsch. verw. Gekiete 69(1985), 439–459. Google Scholar
[22] 22. Sznitman, A.-S., Équations de type de Boltzmann, spatialement homogènes, Wahrsch Z. verw. Gekiete 66(1984), 559–592. Google Scholar
[23] 23. Sznitman, A.-S.,Nonlinear reflecting diffusion process, and the propagation of chaos and fluctuations associated, J. Funct. Anal. 56(1984), 311–336. Google Scholar
[24] 24. Sznitman, A.-S., A fluctuation result for nonlinear diffusions.In: Infinite dimensional analysis and stochastic processes, (Albeverio, S., éd.). Pitman Adv. Publ. Prog. (1985), 145–160. Google Scholar
[25] 25. Sznitman, A.-S., Propagation du chaos, École d'été de probabilité de Saint-Hour, 1989. Google Scholar
[26] 26. Tanaka, H., Propagation of chaos for certain purely discontinuous Markov processes with interaction, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 17(1970), 253–272. Google Scholar
[27] 27. Uchiyama, K., Fluctuations of Markovian systems in Kac's caricature of a Maxwellian gas, J. Math. Soc. Japan 35(1983), 477–499. Google Scholar
[28] 28. Uchiyama, K., A fluctuation problem associated with the Boltzmann equation for a gas molecules with a cutoff potential, Japan J. Math. 9(1983), 27–53. Google Scholar
[29] 29. Wild, E., On Boltzmann's equation in the kinetic theory of gases, Proc. Camb. Phil. Soc. 47( 1951 ), 602–609. Google Scholar
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