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 | |
| Publication status | Published - Sep 1 2014 |
| Externally published | Yes |
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All Science Journal Classification (ASJC) codes
- Analysis
Cite this
Malliavin differentiability of solutions of rough differential equations. / Inahama, Yuzuru.
In: Journal of Functional Analysis, Vol. 267, No. 5, 01.09.2014, p. 1566-1584.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Malliavin differentiability of solutions of rough differential equations
AU - Inahama, Yuzuru
PY - 2014/9/1
Y1 - 2014/9/1
N2 - 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.
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.
UR - http://www.scopus.com/inward/record.url?scp=84904116254&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84904116254&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2014.06.011
DO - 10.1016/j.jfa.2014.06.011
M3 - Article
AN - SCOPUS:84904116254
VL - 267
SP - 1566
EP - 1584
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 5
ER -