On the Functional L\'{e}vy-It\^{o} Stochastic Calculus
Probability
2022-02-25 v2
Abstract
Several versions of It\^{o}'s formula have been obtained in the context of the functional stochastic calculus. Here, we revisit this topic in two ways. First, by defining a notion of derivative along a functional, we extend the setting of the (semimartingale) functional It\^{o}'s formula and corresponding calculus. Second, for L\'{e}vy processes, an optimal local-time based It\^{o}'s formula is obtained. Some quick applications are then given.
Keywords
Cite
@article{arxiv.2112.14221,
title = {On the Functional L\'{e}vy-It\^{o} Stochastic Calculus},
author = {Christian Houdré and Jorge Víquez},
journal= {arXiv preprint arXiv:2112.14221},
year = {2022}
}
Comments
The second version included remark 4.6(iv), improved wording, fixed typos, and included more references