| Issue |
ESAIM: PS
Volume 28, 2024
|
|
|---|---|---|
| Page(s) | 46 - 61 | |
| DOI | https://doi.org/10.1051/ps/2023020 | |
| Published online | 22 February 2024 | |
Self-interacting diffusions: Long-time behaviour and exit-problem in the uniformly convex case
1
Université Jean Monnet, CNRS UMR 5208, Institut Camille Jordan, Maison de l’Université,
10 rue Tréfilerie, CS 82301,
42023
Saint-Étienne Cedex 2,
France
2
INRIA Bordeaux Research Center,
France
3
Université de Lorraine, Institut Elie Cartan de Lorraine, CNRS UMR 7502,
Vandoeuvre-lès-Nancy
F-54506,
France
* Corresponding author: aline.kurtzmann@univ-lorraine.fr
Received:
24
March
2023
Accepted:
7
November
2023
We study a class of time-inhomogeneous diffusion: the self-interacting one. We show a convergence result with a rate of convergence that does not depend on the diffusion coefficient. Finally, we establish a so-called Kramers’ type law for the first exit-time of the process from domain of attractions when the landscapes are uniformly convex.
Mathematics Subject Classification: 60K35 / 60H10 / 60J60
Key words: Self-interacting diffusion / long-time behaviour / exit-time, Kramers’ law / deterministic flow
© The authors. Published by EDP Sciences, SMAI 2024
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