It\^{o}--F\"{o}llmer Calculus in Banach Spaces I: The It\^{o} Formula

Abstract

We prove F\"{o}llmer's pathwise It\^{o} formula for a Banach space-valued c\`{a}dl\`{a}g path. We also relax the assumption on the sequence of partitions along which we treat the quadratic variation of a path.