Elementary coupling approach for non-linear perturbation of Markov processes with mean-field jump mechanims and related problems

Pierre Monmarché

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arXiv · 1809.10953

Elementary coupling approach for non-linear perturbation of Markov processes with mean-field jump mechanims and related problems

Pierre Monmarché

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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.

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Pierre Monmarché. 2018-09-28. Elementary coupling approach for non-linear perturbation of Markov processes with mean-field jump mechanims and related problems. https://arxiv.org/abs/1809.10953

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