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