Malliavin calculus for stochastic differential equations driven by subordinated Brownian motions

Seiichiro Kusuoka

研究成果: Article査読

12 被引用数 (Scopus)

抄録

Malliavin calculus is applicable to functionals of stable processes by using subordination. We prepare Malliavin calculus for stochastic differential equations driven by Brownian motions with deterministic time change, and the conditions that the existence and the regularity of the densities inherit from those of the densities of conditional probabilities. By using these, we prove regularity properties of the solutions of equations driven by subordinated Brownian motions.[4] a similar problem is considered.this article we consider more general cases. We also consider equations driven by rotation-invariant stable processes. We prove that the ellipticity of the equations implies the existence of the density of the solution, and we also prove that the regularity of the coefficients implies the regularity of the densities in the case when the equations are driven by one rotation-invariant stable process.

本文言語English
ページ(範囲)491-520
ページ数30
ジャーナルKyoto Journal of Mathematics
50
3
DOI
出版ステータスPublished - 2010 9

ASJC Scopus subject areas

  • Mathematics(all)

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