Malliavin calculus for stochastic differential equations driven by subordinated Brownian motions

Seiichiro Kusuoka

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)491-520
Number of pages30
JournalKyoto Journal of Mathematics
Volume50
Issue number3
DOIs
Publication statusPublished - Sep 2010
Externally publishedYes

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Malliavin Calculus
Stochastic Equations
Brownian motion
Stable Process
Differential equation
Rotation Invariant
Regularity
Imply
Time Change
Subordination
Ellipticity
Regularity Properties
Conditional probability
Coefficient

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Malliavin calculus for stochastic differential equations driven by subordinated Brownian motions. / Kusuoka, Seiichiro.

In: Kyoto Journal of Mathematics, Vol. 50, No. 3, 09.2010, p. 491-520.

Research output: Contribution to journalArticle

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