Electronic Journal of Probability

A Note on Higher Dimensional p-Variation

Peter Friz and Nicolas Victoir

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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

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

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

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

higher dimensional p-variation Gaussian rough paths

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Friz, Peter; Victoir, Nicolas. A Note on Higher Dimensional p-Variation. Electron. J. Probab. 16 (2011), paper no. 68, 1880--1899. doi:10.1214/EJP.v16-951. https://projecteuclid.org/euclid.ejp/1464820237

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