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

Sylvie Meleard

ESAIM: Probability and Statistics (1998)

  • Volume: 2, page 23-40
  • ISSN: 1292-8100

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Meleard, Sylvie. "Stochastic approximations of the solution of a full Boltzmann equation with small initial data." ESAIM: Probability and Statistics 2 (1998): 23-40. <http://eudml.org/doc/104250>.

@article{Meleard1998,
author = {Meleard, Sylvie},
journal = {ESAIM: Probability and Statistics},
keywords = {Boltzmann equation; existence and uniqueness; nonlinear martingale problem; algorithms; associated mean-field interacting particle systems},
language = {eng},
pages = {23-40},
publisher = {EDP Sciences},
title = {Stochastic approximations of the solution of a full Boltzmann equation with small initial data},
url = {http://eudml.org/doc/104250},
volume = {2},
year = {1998},
}

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
PB - EDP Sciences
VL - 2
SP - 23
EP - 40
LA - eng
KW - Boltzmann equation; existence and uniqueness; nonlinear martingale problem; algorithms; associated mean-field interacting particle systems
UR - http://eudml.org/doc/104250
ER -

References

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  2. CAPRINO, S. and PULVIRENTI, M. ( 1995). A cluster expansion approach to a onedimensional Boltzmann equation: a validity result. Comm. Math. Phys. 166 603-621. Zbl0811.60099MR1312437
  3. CERCIGNANI, C., ILLNER, R. and PULVIRENTI, M. ( 1994). The mathematical theory of dilute gases. Applied math. Sciences, Springer-Verlag, Berlin. Zbl0813.76001MR1307620
  4. 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. Zbl0698.45010MR1014927
  5. GRAHAM, C. and MÉLÉARD, S. ( 1997). Stochastic particle approximations for generalized Boltzmann models and convergence estimates. Ann. Prob. 25 115-132. Zbl0873.60076MR1428502
  6. HAMDACHE, K. ( 1985). Existence in the large and asymptotic behaviour for the Boltzmann equation. Japan J. Appl. Math. 2 65-84. Zbl0653.76053MR839316
  7. JACOD, J. and SHIRYEAV, A.N. ( 1987). Limit theorems for stochastic processes. Springer-Verlag. Zbl0635.60021MR959133
  8. JOFFE, A. and MÉTIVIER, M. ( 1986). Weak convergence of sequences of semimartingales with applications to multitype branching processes. Adv. Appl. Prob. 18 20-65. Zbl0595.60008MR827331
  9. KANIEL, S. and SHINBROT, M. ( 1978). The Boltzmann equation I: uniqueness and global existence. Comm. Math. Phys. 95 117-126. Zbl0371.76061MR475532
  10. 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. Zbl0864.60077MR1431299
  11. MEYER, P.A. ( 1966). Probabilités et Potentiels. Hermann. Zbl0138.10402MR205287
  12. MISCHLER, S. and PERTHAME, B. ( 1997). Boltzmann equation with infinite energy. SIAM J. Math. Analysis 28 1015-1027. Zbl0889.35077MR1466666
  13. NANBU, K. ( 1983). Interrelations between various direct simulation methods for solving the Boltzmann equation. J. Phys. Soc. Japan 52 3382-3388. 
  14. REZAKHZANLOU, F. ( 1996). Kinetic limits for a class ofinteract ing particle systems. Prob. Theory and rel. Fields 104 97-146. Zbl0838.60085MR1367669
  15. SZNITMAN, A.S. ( 1991). Topics in propagation of chaos. École d'été de Probabilités de Saint-Flour XIX - 1989, Lect. Notes in Math. 1464, Springer. Zbl0732.60114MR1108185
  16. TOSCANI, G. ( 1986). On the nonlinear Boltzmann equation in unbounded domains. Arch. Rat. Mech. Anal. 95 37-49. Zbl0661.76077MR849403

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