Malliavin differentiability of solutions of rough differential equations

Yuzuru Inahama

doi:10.1016/j.jfa.2014.06.011

Malliavin differentiability of solutions of rough differential equations

Yuzuru Inahama

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

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 language	English
Pages (from-to)	1566-1584
Number of pages	19
Journal	Journal of Functional Analysis
Volume	267
Issue number	5
DOIs	https://doi.org/10.1016/j.jfa.2014.06.011
Publication status	Published - Sep 1 2014
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis

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10.1016/j.jfa.2014.06.011

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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.",

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AB - 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.

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JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

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ER -

Malliavin differentiability of solutions of rough differential equations

Abstract

All Science Journal Classification (ASJC) codes

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