Elementary coupling approach for non-linear perturbation of Markov processes with mean-field jump mechanims and related problems
Probability
2023-01-16 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1809.10953,
title = {Elementary coupling approach for non-linear perturbation of Markov processes with mean-field jump mechanims and related problems},
author = {Pierre Monmarché},
journal= {arXiv preprint arXiv:1809.10953},
year = {2023}
}