Open Access
Translator Disclaimer
May 2000 Existence and regularity study for two-dimensional Kac equation without cutoff by a probabilistic approach
Nicolas Fournier
Ann. Appl. Probab. 10(2): 434-462 (May 2000). DOI: 10.1214/aoap/1019487350

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

Download 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

Information

Published: May 2000
First available in Project Euclid: 22 April 2002

zbMATH: 1056.60052
MathSciNet: MR1768239
Digital Object Identifier: 10.1214/aoap/1019487350

Subjects:
Primary: 60H07
Secondary: 35B65 , 82C40

Keywords: Boltzmann equation without cutoff , Malliavin calculus for jump processes

Rights: Copyright © 2000 Institute of Mathematical Statistics

JOURNAL ARTICLE
29 PAGES


SHARE
Vol.10 • No. 2 • May 2000
Back to Top