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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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