2014/08/06 by Alberto Ohashi, Ohashi, Alberto, Alexandre B. Simas +1
Computer Science · Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Approximation and Integration #Matrix Theory and Algorithms #Point processes and geometric inequalities #Probability (math.PR) #math.FA #math.PR
paper · pdf · doi:10.48550/arxiv.1408.1428
Some typos are corrected
openalex publication_date 2014/08/06 · arxiv created 2014/08/26 · arxiv updated 2014/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note, we establish a novel maximal inequality of the 2D Young integral ∫ab∫cd FdG in terms of the (p,q)-bivariation norms of the section functions x↦ F(x,y) and y↦ F(x,y) where G:[a,b]× [c,d]→ ℝ is a controlled path satisfying finite (p,q)-variation conditions. The proof is reminiscent from the Young's original ideas \citeyoung1 in defining two-parameter integrals in terms of (p,q)-finite bivariations. Our result complements the standard maximal inequality established by Towghi \citetowghi1 in terms of joint variations. We apply the maximal inequality to get novel strong approximations for 2D Young integrals w.r.t the Brownian local time in terms of number of upcrossings of a given approximating random walk.