no. 4
Strict positivity of the solution to a 2-dimensional spatially homogeneous Boltzmann equation without cutoff
Annales de l'I.H.P. Probabilités et statistiques, Tome 37 (2001) no. 4, pp. 481-502. 
@article{AIHPB_2001__37_4_481_0,
     author = {Fournier, Nicolas},
     title = {Strict positivity of the solution to a $2$-dimensional spatially homogeneous {Boltzmann} equation without cutoff},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {481--502},
     publisher = {Elsevier},
     volume = {37},
     number = {4},
     year = {2001},
     mrnumber = {1876840},
     zbl = {0981.60056},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2001__37_4_481_0/}
}
TY  - JOUR
AU  - Fournier, Nicolas
TI  - Strict positivity of the solution to a $2$-dimensional spatially homogeneous Boltzmann equation without cutoff
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2001
SP  - 481
EP  - 502
VL  - 37
IS  - 4
PB  - Elsevier
UR  - http://www.numdam.org/item/AIHPB_2001__37_4_481_0/
LA  - en
ID  - AIHPB_2001__37_4_481_0
ER  - 
%0 Journal Article
%A Fournier, Nicolas
%T Strict positivity of the solution to a $2$-dimensional spatially homogeneous Boltzmann equation without cutoff
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2001
%P 481-502
%V 37
%N 4
%I Elsevier
%U http://www.numdam.org/item/AIHPB_2001__37_4_481_0/
%G en
%F AIHPB_2001__37_4_481_0
Fournier, Nicolas. Strict positivity of the solution to a $2$-dimensional spatially homogeneous Boltzmann equation without cutoff. Annales de l'I.H.P. Probabilités et statistiques, Tome 37 (2001) no. 4, pp. 481-502. http://www.numdam.org/item/AIHPB_2001__37_4_481_0/

[1] S. Aida, S. Kusuoka, D. Stroock, On the Support of Wiener Functionals, Asymptotic Problems in Probability Theory, 1993. | MR | Zbl

[2] V. Bally, E. Pardoux, Malliavin Calculus for white noise driven SPDEs, Potential Analysis 9 (1) (1998) 27-64. | MR | Zbl

[3] G. Ben Arous, R. Léandre, Décroissance exponentielle du noyau de la chaleur sur la diagonale (II), Probability Theory and Related Fields 90 (1991) 377-402. | MR | Zbl

[4] K. Bichteler, J. Jacod, Calcul de Malliavin pour les diffusions avec sauts, existence d'une densité dans le cas unidimensionel, in: Séminaire de Probabilités XVII, Lecture Notes in Math., 986, Springer Verlag, 1983, pp. 132-157. | Numdam | MR | Zbl

[5] L. Desvillettes, About the regularizing properties of the non cutoff Kac equation, Comm. Math. Physics 168 (1995) 416-440. | MR | Zbl

[6] L. Desvillettes, Regularization properties of the 2-dimensional non radially symmetric non cutoff spatially homogeneous Boltzmann equation for Maxwellian molecules, Trans. Theory Stat. Phys. 26 (1997) 341-357. | MR | Zbl

[7] L. Desvillettes, C. Graham, S. Méléard, Probabilistic interpretation and numerical approximation of a Kac equation without cutoff, Stochastic Processes and their Applications (2000), to appear. | MR | Zbl

[8] Fournier N., Existence and regularity study for a 2-dimensional Kac equation without cutoff by a probabilistic approach, The Annals of Applied Probability, to appear. | Zbl

[9] N. Fournier, Strict positivity of a solution to a Kac equation without cutoff, J. Statist. Phys. (1999), to appear. | Zbl

[10] Fournier N., Strict positivity of the density for Poisson driven S.D.E.s, Stochastics and Stochastics Reports, to appear. | Zbl

[11] C. Graham, S. Méléard, Existence and regularity of a solution to a Kac equation without cutoff using Malliavin Calculus, Comm. Math. Physics (1998), to appear. | MR | Zbl

[12] Y. Ishikawa, Asymptotic behaviour of the transition density for jump type processes in small time, Tohoku Math. J. 46 (1994) 443-456. | MR | Zbl

[13] J. Jacod, Equations différentielles linéaires, la méthode de variation des constantes, in: Séminaire de Probabilités XVI, Lecture Notes in Math., 920, Springer Verlag, 1982, pp. 442-448. | Numdam | MR | Zbl

[14] J. Jacod, A.N. Shiryaev, Limit Theorems for Stochastic Processes, Springer Verlag, 1987. | MR | Zbl

[15] R. Léandre, Densité en temps petit d'un processus de sauts, Séminaire de Probabilités XXI, 1987. | Numdam | Zbl

[16] R. Léandre, Strange behaviour of the heat kernel on the diagonal, in: Albeverio S. (Ed.), Stochastic Processes, Physics and Geometry, World Scientific, 1990, pp. 516-527. | MR

[17] J. Picard, Density in small time at accessible points for jump processes, Stochastic Processes and their Applications 67 (1997) 251-279. | MR | Zbl

[18] A. Pulvirenti, B. Wennberg, A Maxwellian lowerbound for solutions to the Boltzmann equation, Comm. Math. Phys. 183 (1997) 145-160. | MR | Zbl

[19] H. Tanaka, Probabilistic treatment of the Boltzmann equation of Maxwellian molecules, Z.W. 66 (1978) 559-592. | MR | Zbl