Quantitative sensitivity analysis for Fokker-Planck equation with respect to the Wasserstein distance
Year: 2026
Type: preprint
Abstract: We analyze the sensitivity of solutions to the Fokker-Planck equation with respect to some unknown parameter. Our main result is to provide quantitative upper bounds for the $p$-Wasserstein distance $\mathcal{W}_p$ between two solutions with different parameters, for every $p \geq 2$. We are able to give two proofs of this result, the first relying on synchronous coupling between two solutions of an SDE, and another one that relies on the differentiation of Kantorovitch dual formulation of optimal transport. We also provide more specific bounds in the case of the overdamped Langevin process, for which we are able to compare convergence to the invariant measure and sensitivity to the parameter.
Source: arXiv (Cornell University)
Author: Morange, Martin
Institution: ANANKE
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: European Commission
Award: G434337789
OpenAlex ID: W7124673229