Abstract
In this note, we establish that the stationary distribution of a possibly non-equilibrium Langevin diffusion converges, as the damping parameter goes to infinity (or equivalently in the Smoluchowski-Kramers vanishing mass limit), toward a tensor product of the stationary distribution of the corresponding overdamped process and of a Gaussian distribution.
Funding Statement
P. Monmarché acknowledges financial support by the French ANR grants EFI (ANR-17-CE40-0030) and SWIDIMS (ANR-20-CE40-0022) and by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No 810367), project EMC2.
Acknowledgments
Mouad Ramil is currently a postdoc at CEA-DAM in Arpajon (France). The authors thank Gabriel Stoltz for fruitfull discussions.
Funding Statement
P. Monmarché acknowledges financial support by the French ANR grants EFI (ANR-17-CE40-0030) and SWIDIMS (ANR-20-CE40-0022) and by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No 810367), project EMC2.
Acknowledgments
Mouad Ramil is currently a postdoc at CEA-DAM in Arpajon (France). The authors thank Gabriel Stoltz for fruitfull discussions.
Citation
Pierre Monmarché. Mouad Ramil. "Overdamped limit at stationarity for non-equilibrium Langevin diffusions." Electron. Commun. Probab. 27 1 - 8, 2022. https://doi.org/10.1214/22-ECP447
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