Controlled fields, rough stochastic calculus, and It\^o-Wentzell-Alekseev-Gr\"obner identities
Probability
2026-05-05 v2
Abstract
We develop a calculus of space-time controlled fields for rough stochastic systems. This approach provides a unified composition rule for evaluating random fields along rough semimartingales and yields a rough stochastic It\^o-Wentzell formula under natural and verifiable regularity assumptions. Our motivation comes from works of Hudde et al. (2024) and, independently, Del Moral and Singh (2022) where the authors established, respectively, It\^o-Alekseev-Gr\"obner, backward It\^o-Wentzell, and diffusion interpolation formulas.
Keywords
Cite
@article{arxiv.2603.05388,
title = {Controlled fields, rough stochastic calculus, and It\^o-Wentzell-Alekseev-Gr\"obner identities},
author = {Jannis R. Dause and Peter K. Friz and Arnulf Jentzen and Jian Song},
journal= {arXiv preprint arXiv:2603.05388},
year = {2026}
}