@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, Volume 37 (2001) no. 4, pp. 481-502. http://www.numdam.org/item/AIHPB_2001__37_4_481_0/
[1] On the Support of Wiener Functionals, Asymptotic Problems in Probability Theory, 1993. | MR | Zbl
, , ,[2] Malliavin Calculus for white noise driven SPDEs, Potential Analysis 9 (1) (1998) 27-64. | MR | Zbl
, ,[3] Décroissance exponentielle du noyau de la chaleur sur la diagonale (II), Probability Theory and Related Fields 90 (1991) 377-402. | MR | Zbl
, ,[4] 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] About the regularizing properties of the non cutoff Kac equation, Comm. Math. Physics 168 (1995) 416-440. | MR | Zbl
,[6] 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] 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] 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] Existence and regularity of a solution to a Kac equation without cutoff using Malliavin Calculus, Comm. Math. Physics (1998), to appear. | MR | Zbl
, ,[12] Asymptotic behaviour of the transition density for jump type processes in small time, Tohoku Math. J. 46 (1994) 443-456. | MR | Zbl
,[13] 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] Limit Theorems for Stochastic Processes, Springer Verlag, 1987. | MR | Zbl
, ,[15] Densité en temps petit d'un processus de sauts, Séminaire de Probabilités XXI, 1987. | Numdam | Zbl
,[16] Strange behaviour of the heat kernel on the diagonal, in: (Ed.), Stochastic Processes, Physics and Geometry, World Scientific, 1990, pp. 516-527. | MR
,[17] Density in small time at accessible points for jump processes, Stochastic Processes and their Applications 67 (1997) 251-279. | MR | Zbl
,[18] A Maxwellian lowerbound for solutions to the Boltzmann equation, Comm. Math. Phys. 183 (1997) 145-160. | MR | Zbl
, ,[19] Probabilistic treatment of the Boltzmann equation of Maxwellian molecules, Z.W. 66 (1978) 559-592. | MR | Zbl
,