A Note on Higher Dimensional p-Variation

Peter Friz (Technische Universit├Ąt and Weierstrass Institute for Applied Analysis and Stochastics, Berlin)
Nicolas Victoir (New York)

Abstract


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 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.

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Pages: 1880-1899

Publication Date: October 16, 2011

DOI: 10.1214/EJP.v16-951

References

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