## Electronic Journal of Probability

### A Note on Higher Dimensional p-Variation

#### Abstract

We discuss $p$-variation regularity of real-valued functions defined on $[0,T]\times [0,T]$, based on rectangular increments. When $p \gt 1$, there are two slightly different notions of $p$-variation; both of which are useful in the context of Gaussian roug paths. Unfortunately, these concepts were blurred in previous works; the purpose of this note is to show that the afore-mentioned notions of $p$-variations are "epsilon-close". In particular, all arguments relevant for Gaussian rough paths go through with minor notational changes.

#### Article information

Source
Electron. J. Probab., Volume 16 (2011), paper no. 68, 1880-1899.

Dates
Accepted: 16 October 2011
First available in Project Euclid: 1 June 2016

https://projecteuclid.org/euclid.ejp/1464820237

Digital Object Identifier
doi:10.1214/EJP.v16-951

Mathematical Reviews number (MathSciNet)
MR2842090

Zentralblatt MATH identifier
1244.60066

Subjects
Primary: 60H99: None of the above, but in this section

Rights