A biparameter decomposition of Davis–Garsia type
Volume 269 / 2023
Studia Mathematica 269 (2023), 167-191
MSC: Primary 60G42; Secondary 60G46, 42B25. 46E30.
DOI: 10.4064/sm211026-7-7
Published online: 13 October 2022
Abstract
We prove that for any martingale with respect to a biparameter atomic filtration satisfying the $(F_4)$ condition there is a martingale having the same joint distribution but with respect to the canonical $(F_4)$ filtration. Then we prove a biparameter variant of Davis–Garsia decomposition.
