Existence and regularity study for two-dimensional Kac equation without cutoff by a probabilistic approach

Annals of Applied Probability

Volumn 10, Issue 2, 2000, Pages 434-462

  Fournier, Nicolas ^a  

^a SORBONNE UNIVERSITÉ   (France)

Author keywords

Boltzmann equation without cutoff; Malliavin calculus for jump processes

Indexed keywords

EID: 0034401299     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1019487350     Document Type: Article

References (9)

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2. BICHTELER, K. and JACOD, J. (1983). Calcul de Malliavin pour les diffusions avec sauts existence d'une densité dans le cas unidimensionel. Séminaire de Probabilités XVII. Lecture Notes in Math. 986 132-157. Springer, Berlin.
3. DESVILLETTES, L. (1995). Regularization properties of the 2-dimensional non radially symmetric non cutoff spatially homogeneous Boltzmann equation for Maxwellian molecules. Prépublication du Département de mathématique de l'Université d'Orléans.
4. DESVILLETTES, L., GRAHAM, C., and MÉLÉARD S. (1998). Probabilistic interpretation and numerical approximation of a Kac equation without cutoff. Prépublication no 434 du Laboratoire de Probabilités de l'Université Paris VI.
5. GRAHAM, C. and MÉLÉARD, S. (1998). Existence and regularity of a solution to a Kac equation without cutoff using Malliavin calculus. Prépublication no 438 du Laboratoire de Probabilités de l'Université Paris VI.
6. JACOD, J. (1982) Equations différentielles linéaires, la méthode de variation des constantes. Séminaire de Probabilités XVI. Lecture Notes in Math. 920 442-448. Springer, Berlin.
7. JACOD, J. and SHIRYAEV, A.N. (1987). Limit Theorems for Stochastic Processes. Springer, Berlin.
8. NUALART, D. (1995). The Malliavin Calculus and Related Topics, Probability and its Applications. Springer, Berlin.
9. TANAKA, H. (1978). Probabilistic treatment of the Boltzmann equation of Maxwellian molecules. Z. Warsch. Verw. Gebiete. 66 559-592.