| Issue |
ESAIM: PS
Volume 27, 2023
|
|
|---|---|---|
| Page(s) | 278 - 323 | |
| DOI | https://doi.org/10.1051/ps/2023002 | |
| Published online | 15 February 2023 | |
Elementary coupling approach for non-linear perturbation of Markov processes with mean-field jump mechanisms and related problems
Laboratoire Jacques-Louis Lions,
Sorbonne Université 4 place Jussieu
75005
Paris,
France
* Corresponding author: pierre.monmarche@sorbonne-universite.fr
Received:
11
February
2021
Accepted:
13
January
2023
Mean-field integro-differential equations are studied in an abstract framework, through couplings of the corresponding stochastic processes. In the perturbative regime, the equation is proven to admit a unique equilibrium, toward which the process converges exponentially fast. Similarly, in this case, the associated particle system is proven to converge toward its equilibrium at a rate independent from the number of particles.
Mathematics Subject Classification: 60J75
Key words: Mean-field interaction / jump processes / PDMP / interacting particle system / coupling / integro-differential equation
© The authors. Published by EDP Sciences, SMAI 2023
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