Functional It\=o calculus in Hilbert spaces and application to path-dependent Kolmogorov equations
Probability
2018-06-22 v3 Analysis of PDEs
Abstract
Recently, functional It\=o calculus has been introduced and developed in finite dimension for functionals of continuous semimartingales. With different techniques, we develop a functional It\=o calculus for functionals of Hilbert spacevalued diffusions. In this context, we first prove a path-dependent It\=o's formula, then we show applications to classical solutions of path-dependent Kolmogorov equations in Hilbert spaces and derive a Clark-Ocone type formula. Finally, we explicitly verify that all the theory developed can be applied to a class of diffusions driven by SDEs with a path-dependent drift (suitably regular) and constant diffusion coefficient.
Keywords
Cite
@article{arxiv.1606.06326,
title = {Functional It\=o calculus in Hilbert spaces and application to path-dependent Kolmogorov equations},
author = {Mauro Rosestolato},
journal= {arXiv preprint arXiv:1606.06326},
year = {2018}
}