Existence of densities of solutions of stochastic differential equations by Malliavin calculus

Seiichiro Kusuoka

研究成果: Article査読

8 被引用数 (Scopus)

抄録

I considered if solutions of stochastic differential equations have their density or not when the coefficients are not Lipschitz continuous. However, when stochastic differential equations whose coefficients are not Lipschitz continuous, the solutions would not belong to Sobolev space in general. So, I prepared the class Vh which is larger than Sobolev space, and considered the relation between absolute continuity of random variables and the class Vh. The relation is associated to a theorem of N. Bouleau and F. Hirsch. Moreover, I got a sufficient condition for a solution of stochastic differential equation to belong to the class Vh, and showed that solutions of stochastic differential equations have their densities in a special case by using the class Vh.

本文言語English
ページ(範囲)758-784
ページ数27
ジャーナルJournal of Functional Analysis
258
3
DOI
出版ステータスPublished - 2010 2 1

ASJC Scopus subject areas

  • Analysis

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