Malliavin differentiability of solutions of rough differential equations

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Abstract

In this paper we study rough differential equations driven by Gaussian rough paths from the viewpoint of Malliavin calculus. Under mild assumptions on coefficient vector fields and underlying Gaussian processes, we prove that solutions at a fixed time are smooth in the sense of Malliavin calculus. Examples of Gaussian processes include fractional Brownian motion with Hurst parameter larger than 1/4.

Original languageEnglish
Pages (from-to)1566-1584
Number of pages19
JournalJournal of Functional Analysis
Volume267
Issue number5
DOIs
Publication statusPublished - Sep 1 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

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