Existence and regularity of a solution of a Kac equation without cutoff using the stochastic calculus of variations
type: Item
instance of: scholarly article
title: Existence and regularity of a solution of a Kac equation without cutoff using the stochastic calculus of variations
zbMATH Open document ID: 0953.60057
author: Carl Graham
author: Sylvie Méléard
published in: Communications in Mathematical Physics
publication date: 1999-12-16T00:00:00Z
review text: The authors study a Kac-type equation without cutoff with which they associate a nonlinear stochastic differential equation. The stochastic calculus of variations allows them to prove, inspired in a previous paper by Jacod and Bichteler, that the law of the solution to the aforementioned stochastic differential equation has a density with respect to Lebesgue measure, which is a solution to the Kac equation. They allow the initial law to be rather general by demanding only the existence of its second moment. This leads to a significant improvement of previous results on the existence of solutions to Kac-type equations. Moreover, they show that better results on the smoothness of the density are obtained if all the moments exist for the initial law.
Mathematics Subject Classification ID: 60H99
Mathematics Subject Classification ID: 82C99
zbMATH DE Number: 1379887
zbMATH Keywords: stochastic differential equations
zbMATH Keywords: Malliavin calculus
reviewed by: Rolando Rebolledo
MaRDI profile type: Publication
full work available at URL: s002200050689
OpenAlex ID: W2007762741
DOI: 10.1007/S002200050689
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description: scientific article; zbMATH DE number 1379887