We consider a two-dimensional Kac equation without cutoff,which we
relate to a stochastic differential equation.We prove the existence of a
solution for this SDE, and we use the Malliavin calculus (or stochastic
calculus of variations) to prove that the law of this solution admits a smooth
density with respect to the Lebesgue measure on $\mathbf{R}^2$.This density
satisfies the Kac equation.
Publié le : 2000-05-14
Classification:
Boltzmann equation without cutoff,
Malliavin calculus for jump processes,
60H07,
82C40,
35B65
@article{1019487350,
author = {Fournier, Nicolas},
title = {Existence and regularity study for two-dimensional Kac equation
without cutoff by a probabilistic approach},
journal = {Ann. Appl. Probab.},
volume = {10},
number = {2},
year = {2000},
pages = { 434-462},
language = {en},
url = {http://dml.mathdoc.fr/item/1019487350}
}
Fournier, Nicolas. Existence and regularity study for two-dimensional Kac equation
without cutoff by a probabilistic approach. Ann. Appl. Probab., Tome 10 (2000) no. 2, pp. 434-462. http://gdmltest.u-ga.fr/item/1019487350/