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Volumn 161, Issue 1-2, 2015, Pages 1-59

A new approach to quantitative propagation of chaos for drift, diffusion and jump processes

Author keywords

Boltzmann equation; Drift diffusion; Fluctuations; Granular gas; Inelastic collision; McKean Vlasov equation; Mean field limit; Quantitative

Indexed keywords


EID: 84889028233     PISSN: 01788051     EISSN: 14322064     Source Type: Journal    
DOI: 10.1007/s00440-013-0542-8     Document Type: Article
Times cited : (78)

References (40)
  • 1
    • 34249924419 scopus 로고
    • The homogeneous Boltzmann hierarchy and statistical solutions to the homogeneous Boltzmann equation
    • Arkeryd, L., Caprino, S., Ianiro, N.: The homogeneous Boltzmann hierarchy and statistical solutions to the homogeneous Boltzmann equation. J. Stat. Phys. 63(1–2), 345–361 (1991)
    • (1991) J. Stat. Phys , vol.63 , Issue.1-2 , pp. 345-361
    • Arkeryd, L.1    Caprino, S.2    Ianiro, N.3
  • 2
    • 33748908493 scopus 로고    scopus 로고
    • Contractive metrics for a Boltzmann equation for granular gases: diffusive equilibria
    • Bisi, M., Carrillo, J.A., Toscani, G.: Contractive metrics for a Boltzmann equation for granular gases: diffusive equilibria. J. Stat. Phys. 118(1–2), 301–331 (2005)
    • (2005) J. Stat. Phys , vol.118 , Issue.1-2 , pp. 301-331
    • Bisi, M.1    Carrillo, J.A.2    Toscani, G.3
  • 3
    • 0034343060 scopus 로고    scopus 로고
    • On some properties of kinetic and hydrodynamic equations for inelastic interactions
    • Bobylev, A.V., Carrillo, J.A., Gamba, I.M.: On some properties of kinetic and hydrodynamic equations for inelastic interactions. J. Stat. Phys. 98(3–4), 743–773 (2000)
    • (2000) J. Stat. Phys , vol.98 , Issue.3-4 , pp. 743-773
    • Bobylev, A.V.1    Carrillo, J.A.2    Gamba, I.M.3
  • 4
    • 35348860787 scopus 로고    scopus 로고
    • Tanaka theorem for inelastic Maxwell models
    • Bolley, F., Carrillo, J.A.: Tanaka theorem for inelastic Maxwell models. Commun. Math. Phys. 276(2), 287–314 (2007)
    • (2007) Commun. Math. Phys , vol.276 , Issue.2 , pp. 287-314
    • Bolley, F.1    Carrillo, J.A.2
  • 5
    • 77956719419 scopus 로고    scopus 로고
    • Trend to equilibrium and particle approximation for a weakly selfconsistent Vlasov–Fokker–Planck equation
    • Bolley, F., Guillin, A., Malrieu, F.: Trend to equilibrium and particle approximation for a weakly selfconsistent Vlasov–Fokker–Planck equation. M2AN Math. Model. Numer. Anal. 44(5), 867–884 (2010)
    • (2010) M2AN Math. Model. Numer. Anal , vol.44 , Issue.5 , pp. 867-884
    • Bolley, F.1    Guillin, A.2    Malrieu, F.3
  • 6
    • 39149098246 scopus 로고    scopus 로고
    • Contractive probability metrics and asymptotic behavior of dissipative kinetic equations
    • Carrillo, J., Toscani, G.: Contractive probability metrics and asymptotic behavior of dissipative kinetic equations. Rivista Matemàtica di Parma 6, 75–198 (2007)
    • (2007) Rivista Matemàtica di Parm , vol.6 , pp. 75-198
    • Carrillo, J.1    Toscani, G.2
  • 7
    • 0034504071 scopus 로고    scopus 로고
    • Steady states of a Boltzmann equation for driven granular media
    • Carrillo, J.A., Cercignani, C., Gamba, I.M.: Steady states of a Boltzmann equation for driven granular media. Phys. Rev. E (3) 62(6, part A), 7700–7707 (2000)
    • (2000) Phys. Rev. E (3 , vol.62 , Issue.6 , pp. 7700-7707
    • Carrillo, J.A.1    Cercignani, C.2    Gamba, I.M.3
  • 8
    • 1542399709 scopus 로고    scopus 로고
    • Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates
    • Carrillo, J.A., McCann, R.J., Villani, C.: Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates. Rev. Mat. Iberoamericana 19(3), 971–1018 (2003)
    • (2003) Rev. Mat. Iberoamerican , vol.19 , Issue.3 , pp. 971-1018
    • Carrillo, J.A.1    McCann, R.J.2    Villani, C.3
  • 9
    • 84948251446 scopus 로고
    • On the Boltzmann equation for rigid spheres
    • Cercignani, C.: On the Boltzmann equation for rigid spheres. Transport Theory Stat. Phys. 2(3), 211–225 (1972)
    • (1972) Transport Theory Stat. Phys , vol.2 , Issue.3 , pp. 211-225
    • Cercignani, C.1
  • 14
    • 33845682081 scopus 로고    scopus 로고
    • Uniqueness for a class of spatially homogeneous Boltzmann equations without angular cutoff
    • Fournier, N.: Uniqueness for a class of spatially homogeneous Boltzmann equations without angular cutoff. J. Stat. Phys. 125(4), 927–946 (2006)
    • (2006) J. Stat. Phys , vol.125 , Issue.4 , pp. 927-946
    • Fournier, N.1
  • 15
    • 84869121543 scopus 로고    scopus 로고
    • Asymptotic of grazing collisions and particle approximation for the Kac equation without cutoff
    • Fournier, N., Godinho, D.: Asymptotic of grazing collisions and particle approximation for the Kac equation without cutoff. Commun. Math. Phys. 316, 307–344 (2012)
    • (2012) Commun. Math. Phy , vol.316 , pp. 307-344
    • Fournier, N.1    Godinho, D.2
  • 16
    • 21844510511 scopus 로고
    • Metrics for probability distributions and the trend to equilibrium for solutions of the Boltzmann equation
    • Gabetta, G., Toscani, G., Wennberg, B.: Metrics for probability distributions and the trend to equilibrium for solutions of the Boltzmann equation. J. Stat. Phys. 81(5–6), 901–934 (1995)
    • (1995) J. Stat. Phys , vol.81 , Issue.5-6 , pp. 901-934
    • Gabetta, G.1    Toscani, G.2    Wennberg, B.3
  • 17
    • 0001294845 scopus 로고
    • Principles of the kinetic theory of gases
    • Thermodynamik der Gase. Springer, Berlin:
    • Grad, H.: Principles of the kinetic theory of gases. In: Handbuch der Physik (herausgegeben von S. Flügge), Bd. 12, Thermodynamik der Gase. Springer, Berlin (1958)
    • (1958) Handbuch der Physik (herausgegeben von S. Flügge), B , pp. 12
    • Grad, H.1
  • 19
    • 0040831290 scopus 로고    scopus 로고
    • Stochastic particle approximations for generalized Boltzmann models and convergence estimates
    • Graham, C., Méléard, S.: Stochastic particle approximations for generalized Boltzmann models and convergence estimates. Ann. Probab. 25(1), 115–132 (1997)
    • (1997) Ann. Probab , vol.25 , Issue.1 , pp. 115-132
    • Graham, C.1    Méléard, S.2
  • 20
    • 38349102784 scopus 로고    scopus 로고
    • Graham, C., Méléard, S.: In: CEMRACS (Orsay), volume 10 of ESAIM Proc. Soc. Math. Appl. Indust., Paris, pp. 77–126 (1999, electronic)
    • Graham, C., Méléard, S.: Probabilistic tools and Monte-Carlo approximations for some Boltzmann equations. In: CEMRACS 1999 (Orsay), volume 10 of ESAIM Proc. Soc. Math. Appl. Indust., Paris, pp. 77–126 (1999, electronic)
    • (1999) Probabilistic tools and Monte-Carlo approximations for some Boltzmann equations
  • 21
    • 0002379667 scopus 로고
    • Propagation of chaos for the Boltzmann equation
    • Grünbaum, F.A.: Propagation of chaos for the Boltzmann equation. Arch. Ration. Mech. Anal. 42, 323–345 (1971)
    • (1971) Arch. Ration. Mech. Anal , vol.42 , pp. 323-345
    • Grünbaum, F.A.1
  • 22
    • 0001467016 scopus 로고
    • Global validity of the Boltzmann equation for a two-dimensional rare gas in vacuum
    • Illner, R., Pulvirenti, M.: Global validity of the Boltzmann equation for a two-dimensional rare gas in vacuum. Commun. Math. Phys. 105(2), 189–203 (1986)
    • (1986) Commun. Math. Phys , vol.105 , Issue.2 , pp. 189-203
    • Illner, R.1    Pulvirenti, M.2
  • 28
    • 21144445368 scopus 로고    scopus 로고
    • Convergence to equilibrium for granular media equations and their Euler schemes
    • Malrieu, F.: Convergence to equilibrium for granular media equations and their Euler schemes. Ann. Appl. Probab. 13(2), 540–560 (2003)
    • (2003) Ann. Appl. Probab , vol.13 , Issue.2 , pp. 540-560
    • Malrieu, F.1
  • 29
    • 0002166759 scopus 로고
    • An exponential formula for solving Boltmann’s equation for a Maxwellian gas
    • McKean Jr, H.P.: An exponential formula for solving Boltmann’s equation for a Maxwellian gas. J. Combin. Theory 2, 358–382 (1967)
    • (1967) J. Combin. Theor , vol.2 , pp. 358-382
    • McKean, H.P.1
  • 31
    • 85016704250 scopus 로고    scopus 로고
    • Master research course “introduction aux limites de champ moyen pour des systèmes de particules
    • Mischler, S.: Master research course “introduction aux limites de champ moyen pour des systèmes de particules”. cel-00576329 (2010)
    • (2010) cel-0057632
    • Mischler, S.1
  • 32
    • 84879420862 scopus 로고    scopus 로고
    • Kac’s program in kinetic theory. Preprint arXiv: 1001.2994
    • Mischler, S., Mouhot, C.: Kac’s program in kinetic theory. Preprint arXiv: 1001.2994. Inventiones Matematicae 193(1), 1–147 (2013)
    • (2013) Inventiones Matematica , vol.193 , Issue.1 , pp. 1-147
    • Mischler, S.1    Mouhot, C.2
  • 34
    • 85016705154 scopus 로고    scopus 로고
    • Rüschendorf
    • Probability and its Applications (New York). Springer, New York:
    • Rachev, S.T., Rüschendorf, L.: Mass Transportation Problems, vol. II. Probability and its Applications (New York). Springer, New York (1998)
    • (1998) L.: Mass Transportation Problem
    • Rachev, S.T.1
  • 35
    • 34250138528 scopus 로고
    • Équations de type de Boltzmann, spatialement homogènes
    • Sznitman, A.-S.: Équations de type de Boltzmann, spatialement homogènes. Z. Wahrsch. Verw. Gebiete 66(4), 559–592 (1984)
    • (1984) Z. Wahrsch. Verw. Gebiet , vol.66 , Issue.4 , pp. 559-592
    • Sznitman, A.-S.1
  • 38
    • 0033072701 scopus 로고    scopus 로고
    • Probability metrics and uniqueness of the solution to the Boltzmann equation for a Maxwell gas
    • Toscani, G., Villani, C.: Probability metrics and uniqueness of the solution to the Boltzmann equation for a Maxwell gas. J. Stat. Phys. 94(3–4), 619–637 (1999)
    • (1999) J. Stat. Phys , vol.94 , Issue.3-4 , pp. 619-637
    • Toscani, G.1    Villani, C.2


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