Path-dependent processes from signatures
Probability
2025-11-04 v2
Abstract
We provide explicit series expansions to certain stochastic path-dependent integral equations in terms of the path signature of the time augmented driving Brownian motion. Our framework encompasses a large class of stochastic linear Volterra and delay equations and in particular the fractional Brownian motion with a Hurst index . Our expressions allow to disentangle an infinite dimensional Markovian structure and open the door to straightforward and simple approximation schemes, that we illustrate numerically.
Cite
@article{arxiv.2407.04956,
title = {Path-dependent processes from signatures},
author = {Eduardo Abi Jaber and Louis-Amand Gérard and Yuxing Huang},
journal= {arXiv preprint arXiv:2407.04956},
year = {2025}
}