Year: 2026
Type: preprint
Abstract: We prove that any two Lévy processes on $\mathbb{R}^d$ with finite second moments admit a coupling that is itself a Lévy process and is both locally and globally optimal for the quadratic cost among all immersion couplings. This strengthens the optimality result of Kang and Lim (2025), which was established among Feller couplings. Our approach uses a martingale criterion for local optimality that applies more generally to Markov processes. The argument rests on the existence of an optimal Lévy coupling and a dual formulation of the associated optimization problem, both previously established by Kang and Lim (2025). We give simpler, self-contained proofs of these two results using optimal transport between infinitely divisible measures and Lassonde's minimax principle.
Source: arXiv (Cornell University)
Authors: Lim, Tau Shean, Ooi, Ray Shua
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7165768968