Stochastic approximations of the solution of a full boltzmann equation with small initial data

ESAIM - Probability and Statistics

Volumn 2, Issue , 1998, Pages 23-40

  Meleard, Sylvie ^a,b  

^a UNIVERSITÉ PARIS OUEST NANTERRE LA DÉFENSE   (France)

^b SORBONNE UNIVERSITÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84996129337     PISSN: 12928100     EISSN: 12623318     Source Type: Journal    
DOI: 10.1051/ps:1998102     Document Type: Article

References (18)

1. Babovsky, H. and ILLNER, R. (1989). A convergence proof for Nanbu’s simulation method for the full Boltzmann equation. SIAM J. Numer. Anal. 26 45-65.
2. BELLOMO, N. and TOSCANI, G. (1985). On the Cauchy problem for the nonlinear Boltzmann equation. Global existence, uniquenss and asymptotic stability. J. Math. Phys. 26.
3. BELLOMO, N., Palczewski, A. and Toscani, G. (1988). Mathematical topics in nonlinear kinetic theory. World scientific, Singapore.
4. CAPRINO, S. and Pulvirenti, M. (1995). A cluster expansion approach to a onedimensional Boltzmann equation: a validity result. Comm. Math. Phys. 166 603-621.
5. CERCIGNANI, C., Illner, R. and PULVIRENTI, M. (1994). The mathematical theory of dilute gases. Applied math. Sciences, Springer-Verlag, Berlin.
6. DiPerna, R. J. and Lions P-L. (1989). On the Cauchy problem for Boltzmann equations: global existence and weak stability. Ann. Math. 130 321-366.
7. Graham, C. and Meleard, S. (1997). Stochastic particle approximations for generalized Boltzmann models and convergence estimates. Ann. Prob. 25 115-132.
8. HAMDACHE, K. (1985). Existence in the large and asymptotic behaviour for the Boltzmann equation. Japan J. Appl. Math. 2 65-84.
9. JACOD, J. and SHIRYEAV, A.N. (1987). Limit theorems for stochastic processes. SpringerVerlag.
10. Joffe, A. and Métivier, M. (1986). Weak convergence of sequences of semimartingales with applications to multitype branching processes. Adv. Appl. Prob. 18 20-65.
11. Kaniel, S. and SHINBROT, M. (1978). The Boltzmann equation I: uniqueness and global existence. Comm. Math. Phys. 95 117-126.
12. MÉLÉARD, S. (1996). Asymptotic behaviour of some interacting particle systems, McKean-Vlasov and Boltzmann models. CIME 1995: Probabilistic models for nonlinear pde’s, Lect. Notes in Math. 1627, Springer.
13. Meyer, P.A. (1966). Probabilités et Potentiels. Hermann.
14. Mischler, S. and PERTHAME, B. (1997). Boltzmann equation with infinite energy. SIAM J. Math. Analysis 28 1015-1027.
15. Nanbu, K. (1983). Interrelations between various direct simulation methods for solving the Boltzmann equation. J. Phys. Soc. Japan 52 3382-3388.
16. Rezakhzanlou, F. (1996). Kinetic limits for a class of interacting particle systems. Prob. Theory and rel. Fields 104 97-146.
17. Sznitman, A.S. (1991). Topics in propagation of chaos. Ecole d’été de Probabilités de Saint-Flour XIX - 1989, Lect. Notes in Math. 1464, Springer.
18. TOSCANI, G. (1986). On the nonlinear Boltzmann equation in unbounded domains. Arch. Rat. Mech. Anal. 95 37-49.