PreprintCC BY 4.0arXiv
Wasserstein bounds for invariant measures in the Smoluchowski-Kramers approximation with stable noise
Abstract
We study invariant position distributions in the Smoluchowski-Kramers approximation for Langevin equations driven by rotationally symmetric α-stable noise, with α∈(1,2). Under global Lipschitz continuity and dissipativity of the drift, we establish a Wasserstein-1 bound of order m1/α between the invariant position distribution of the underdamped system and the invariant distribution of its overdamped limit, where m>0 is the mass parameter. The proof combines a corrected-position test function with a regularized Stein equation. Cancellation of the transport and friction terms reduces the comparison to a first-moment estimate for the stationary velocity.
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BibTeX
@misc{jin2026wasserstein,
title = {{Wasserstein bounds for invariant measures in the Smoluchowski-Kramers approximation with stable noise}},
author = {Xinghu Jin and Wenxuan Tao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32217},
eprint = {2610.32217},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32217},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Wasserstein bounds for invariant measures in the Smoluchowski-Kramers approximation with stable noise
AU - Xinghu Jin
AU - Wenxuan Tao
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32217
UR - https://arxiv.org/abs/2610.32217
AB - We study invariant position distributions in the Smoluchowski-Kramers approximation for Langevin equations driven by rotationally symmetric α-stable noise, with α∈(1,2). Under global Lipschitz continuity and dissipativity of the drift, we establish a Wasserstein-1 bound of order m^1/α between the invariant position distribution of the underdamped system and the invariant distribution of its overdamped limit, where m>0 is the mass parameter. The proof combines a corrected-position test function with a regularized Stein equation. Cancellation of the transport and friction terms reduces the comparison to a first-moment estimate for the stationary velocity.
ER -