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A Note on Higher Dimensional p-Variation


 
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1. Title Title of document A Note on Higher Dimensional p-Variation
 
2. Creator Author's name, affiliation, country Peter Friz; Technische Universität and Weierstrass Institute for Applied Analysis and Stochastics, Berlin; Germany
 
2. Creator Author's name, affiliation, country Nicolas Victoir; New York; United Kingdom
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) higher dimensional p-variation, Gaussian rough paths
 
3. Subject Subject classification 60H99
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) European Union's Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement nr. 258237
 
7. Date (YYYY-MM-DD) 2011-10-16
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/951
 
10. Identifier Digital Object Identifier 10.1214/EJP.v16-951
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 16
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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