@article{PS_1998__2__23_0, author = {Meleard, Sylvie}, title = {Stochastic approximations of the solution of a full {Boltzmann} equation with small initial data}, journal = {ESAIM: Probability and Statistics}, pages = {23--40}, publisher = {EDP-Sciences}, volume = {2}, year = {1998}, mrnumber = {1612167}, zbl = {0980.62069}, language = {en}, url = {http://www.numdam.org/item/PS_1998__2__23_0/} }
TY - JOUR AU - Meleard, Sylvie TI - Stochastic approximations of the solution of a full Boltzmann equation with small initial data JO - ESAIM: Probability and Statistics PY - 1998 SP - 23 EP - 40 VL - 2 PB - EDP-Sciences UR - http://www.numdam.org/item/PS_1998__2__23_0/ LA - en ID - PS_1998__2__23_0 ER -
Meleard, Sylvie. Stochastic approximations of the solution of a full Boltzmann equation with small initial data. ESAIM: Probability and Statistics, Tome 2 (1998), pp. 23-40. http://www.numdam.org/item/PS_1998__2__23_0/
Mathematical topics in nonlinear kinetic theory. World scientific, Singapore. | MR | Zbl
, and ( 1988).A cluster expansion approach to a onedimensional Boltzmann equation: a validity result. Comm. Math. Phys. 166 603-621. | MR | Zbl
and ( 1995).The mathematical theory of dilute gases. Applied math. Sciences, Springer-Verlag, Berlin. | MR | Zbl
, and ( 1994).On the Cauchy problem for Boltzmann equations: global existence and weak stability. Ann. Math. 130 321-366. | MR | Zbl
and ( 1989).Stochastic particle approximations for generalized Boltzmann models and convergence estimates. Ann. Prob. 25 115-132. | MR | Zbl
and ( 1997).Existence in the large and asymptotic behaviour for the Boltzmann equation. Japan J. Appl. Math. 2 65-84. | MR | Zbl
( 1985).Limit theorems for stochastic processes. Springer-Verlag. | MR | Zbl
and ( 1987).Weak convergence of sequences of semimartingales with applications to multitype branching processes. Adv. Appl. Prob. 18 20-65. | MR | Zbl
and ( 1986).The Boltzmann equation I: uniqueness and global existence. Comm. Math. Phys. 95 117-126. | MR | Zbl
and ( 1978).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. | MR | Zbl
( 1996).Probabilités et Potentiels. Hermann. | MR | Zbl
( 1966).Boltzmann equation with infinite energy. SIAM J. Math. Analysis 28 1015-1027. | MR | Zbl
and ( 1997).Interrelations between various direct simulation methods for solving the Boltzmann equation. J. Phys. Soc. Japan 52 3382-3388.
( 1983).Kinetic limits for a class ofinteract ing particle systems. Prob. Theory and rel. Fields 104 97-146. | MR | Zbl
( 1996).Topics in propagation of chaos. École d'été de Probabilités de Saint-Flour XIX - 1989, Lect. Notes in Math. 1464, Springer. | MR | Zbl
( 1991).On the nonlinear Boltzmann equation in unbounded domains. Arch. Rat. Mech. Anal. 95 37-49. | MR | Zbl
( 1986).