The It{ô}-Föllmer formula -- nonstandard cases (2508.14617v1)

Abstract: The purpose of this note is to prove the It{^o}-F\"ollmer formula for the c`adl`ag 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 F\"ollmer, also relaxing restrictions imposed on a sequence of partitions in other related literature.