Existence and regularity study for two-dimensional Kac equation without cutoff by a probabilistic approach
成果类型：
Article
署名作者：
Fournier, N
署名单位：
Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
发表日期：
2000
页码：
434-462
关键词：
摘要：
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 R-2. This density satisfies the Kac equation.