On stochastics equations with respect to semimartingales ii. itô formula in banach spaces

Publisher Website
Google Scholar
Abstract
In the second part of this study a general Itô formula is proved in Banach spaces. A special case reads as follows. Let be a triple of spaces (V is a Banach space with its dual V *, H is a Hilbert space) with continuous dense injections. Consider a V *-valued semi-martingale y of the form on a complete probability space (Ω,FP) endowed with a filtration where V * is a V *-valued progressively measurable process, A is a real-valued nondecreasing adapted cadlag process and h is an H-valued locally square integrable martingale. Suppose that y = v (up to a dP×dA(t) null-set) for a v-valued progressively measurable process v, and that are almost surely locally integrable with respect to dA(t). Then, up to indistinguishability, y is an H-valued adapted cadlag process and the Itô formula is valid for .

This publication has 4 references indexed in Scilit: