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






