2024/12/21 by Xing Gao, Nannan Li, Gao, Xing +3 · 2 citations
Environmental Science · Mathematics · #05C05 #34K50 #37H10 #60H99 #60L20 #60L50 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Hydrology and Watershed Management Studies #Mathematical Dynamics and Fractals #Probability (math.PR) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2412.16479
openalex publication_date 2024/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The universal limit theorem is a central result in rough path theory, which has been proved for: (i) rough paths with roughness (1)/(3)< α≤ (1)/(2); (ii) geometric rough paths with roughness 0< α≤ 1; (iii) branched rough paths with roughness 0< α≤ 1. Planarly branched rough paths are natural generalizations of both rough paths and branched rough paths, in the sense that post-Lie algebras are generalizations of both Lie algebras and pre-Lie algebras. Here the primitive elements of the graded dual Hopf algebra of the Hopf algebra corresponding to the planarly branched rough paths (resp. rough paths, resp. branched rough paths) form a post-Lie (resp. Lie, resp. pre-Lie algebra). In this paper, we prove the universal limit theorem for planarly branched rough paths with roughness (1)/(4)< α≤ (1)/(3), via the method of Banach fixed point theorem.