2011/02/22 by Peter K. Friz, Friz, Peter, Nicolas Victoir +1 · 1 citation
Mathematics · #Advanced Harmonic Analysis Research #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Approximation and Integration #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1102.4587
openalex publication_date 2011/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We discuss p-variation regularity of real-valued functions defined on [0,T]2, 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 aforementioned notions of p-variations are "ε-close". In particular, all arguments relevant for Gaussian rough paths go through with minor notational changes.