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.
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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},
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year = {2001},
zbl = {0981.60056},
mrnumber = {1876840},
language = {en},
url = {http://www.numdam.org/item/AIHPB_2001__37_4_481_0/}
}
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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] 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