A note on higher dimensional \(p\)-variation. (English) Zbl 1244.60066

Friz, Peter; Victoir, Nicolas

Electron. J. Probab. 16, Paper No. 68, 1880-1899 (2011).

Summary: We discuss \(p\)-variation regularity of real-valued functions defined on \([0,T]\times [0,T]\), based on rectangular increments. When \(p>1\), there are two slightly different notions of \(p\)-variation; both of which are useful in the context of Gaussian rough 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.

MSC:

60H99	Stochastic analysis
60G15	Gaussian processes
60G17	Sample path properties

Keywords:

higher dimensional \(p\)-variation; Gaussian rough paths