Strict positivity of a solution to a one-dimensional Kac equation without cutoff

Journal of Statistical Physics

Volumn 99, Issue 3-4, 2000, Pages 725-749

  Fournier, Nicolas ^a  

^a SORBONNE UNIVERSITÉ   (France)

Author keywords

Boltzmann equation without cutoff; Poisson measure; Stochastic calculus of variations

Indexed keywords

EID: 0034178412     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1018683226672     Document Type: Article

References (16)

1. S. Aida, S. Kusuoka, and D. Stroock, On the support of Wiener functionals, Asymptotic Problems in Probability Theory, 1993.
2. A. A. Arsen'ev and O. E. Buryak, On the connexion between a solution of the Boltzmann equation and a solution of the Landau Fokker-Planck equation, Math. USSR Shornik 69(2):465-478 (1991).
3. V. Bally and E. Pardoux, Malliavin calculus for white noise driven SPDEs, Potential Analysis.
4. G. Ben Arous and R. Léandre, Décroissance exponantielle du noyau de la chaleur sur la diagonale (II), Probability Theory and Related Fields 90:377-402 (1991).
5. K. Bichteler and J. Jacod, Calcul de Malliavin pour les diffusions avec sauts, existence d'une densité dans le cas unidimensionel, Séminaire de Probabilités XVII, L.N.M. 986, pp. 132-157 (Springer Verlag, 1983).
6. L. Desvillettes, About the regularizing properties of the non cutoff Kac equation, Comm. Math. Physics 168:416-440, (1995).
7. L. Desvillettes, Regularization properties of the 2-dimensional non radially symmetric non cutoff spatially homogeneous Boltzmann equation for Maxwellian molecules, Prépublication du Département de mathématiques de l'Université d'Orléans, 1995.
8. L. Desvillettes, C. Graham, and S. Méléard, Probabilistic interpretation and numerical approximation of a Kac equation without cutoff, to appear in Stoch. Pro. Appl.
9. N. Fournier, Existence and regularity study for a 2-dimensional Kac equation without cutoff by a probabilistic approach, to appear in Ann. Appl. Prob.
10. N. Fournier, Strict positivity of the density for Poisson driven S.D.E.s, to appear in Stochastics and Stoch. Reports.
11. C. Graham and S. Méléard, Existence and regularity of a solution to a Kac equation without cutoff using Malliavin Calculus, to appear in Communication in Math. Physics.
12. J. Jacod, Equations différentielles linéaires, la méthode de variation des constantes, Séminaire de Probabilités XVI, L.N.M. 920, pp. 442-448 (Springer Verlag, 1982).
13. J. Jacod and A. N. Shiryaev, Limit Theorems for Stochastic Processes (Springer Verlag, 1987).
14. A. Pulvirenti and B. Wennberg, A Maxwellian lowerbound for solutions to the Boltzmann equation, Communication in Math. Phys. 183:145-160 (1997).
15. H. Tanaka, Probabilistic treatment of the Boltzmann equation of Maxwellian molecules, Z.W. 66:559-592 (1978).
16. C. Villani, Contribution à l'étude mathématique des équations de Boltzmann et Landau en théorie cinétique des gaz et des plasmas, Thèse de l'université Paris 9, 1998.