| Issue |
ESAIM: COCV
Volume 32, 2026
|
|
|---|---|---|
| Article Number | 53 | |
| Number of page(s) | 21 | |
| DOI | https://doi.org/10.1051/cocv/2026035 | |
| Published online | 07 July 2026 | |
Itô–Wentzell formulas for semimartingale conditional laws with applications to mean-field control
1
Laboratoire de Probabilités, Statistiques et Modélisation, Université Paris-Cité, France
2
Tandon School of Engineering, New York University, USA
* Corresponding author: mtalbi@lpsm.paris
Received:
3
October
2025
Accepted:
28
April
2026
Abstract
The present paper is an extension of [A. Fadle and N. Touzi, Preprint arXiv:2404.11010 (2024)]. Following the same methodology, merely based on Taylor expansions, we establish the Itô and Itô–Wentzell formulae for flows of conditional distributions of general semimartingales, thus allowing for discontinuous semimartingales with possibly discontinuous flows of conditional marginals. We apply these results to derive the dynamic programming equations corresponding to mean field control problems with Poisson type common noise and mean field stopping problems with common noise.
Mathematics Subject Classification: 60G40 / 49N80 / 35Q89 / 60H30
Key words: Itô formula / Itô–Wentzell formula Wasserstein space / mean field optimal control / mean field optimal stopping
© The authors. Published by EDP Sciences, SMAI 2026
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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