2025/08/20 by W. M. Bednorz, Bednorz, W. M., Rafał M. Łochowski +7
Computer Science · Mathematics · #60H05 #Advanced Topology and Set Theory #Classical Analysis and ODEs (math.CA) #Computability, Logic, AI Algorithms #FOS: Mathematics #Mathematical and Theoretical Analysis #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2508.14617
openalex publication_date 2025/08/20 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28
The purpose of this note is to prove the Itô-Föllmer formula for the càdlàg paths possessing quadratic variation in a possibly ``weakest'' sense along some sequence of partitions. By this we mean, for example, that we do not require the jumps of the quadratic variation to occur exactly at the times when the path itself jumps or that the quadratic variation exists at all time instances. Moreover, we deal with more general partitions than partitions with vanishing mesh used by Föllmer, also relaxing restrictions imposed on a sequence of partitions in other related literature.