Abstract
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.
Citation
Nicolas Fournier. "Existence and regularity study for two-dimensional Kac equation without cutoff by a probabilistic approach." Ann. Appl. Probab. 10 (2) 434 - 462, May 2000. https://doi.org/10.1214/aoap/1019487350
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