Abstract
We study a class of one-dimensional particle systems with true (Bird type) binary interactions, which includes Kac'smodel of the Boltzmann equation and nonlinear equations for the evolution of wealth distribution arising in kinetic economic models. We obtain explicit rates of convergence for the Wasserstein distance between the law of the particles and their limiting law, which are linear in time and depend in a mild polynomial manner on the number of particles. The proof is based on a novel coupling between the particle system and a suitable system of nonindependent nonlinear processes, as well as on recent sharp estimates for empirical measures.
Original language | English |
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Pages (from-to) | 892-916 |
Number of pages | 25 |
Journal | Annals of Applied Probability |
Volume | 26 |
Issue number | 2 |
DOIs | |
Publication status | Published - Apr 2016 |
Keywords
- Kac equation
- Optimal coupling
- Propagation of chaos
- Stochastic particle systems
- Wasserstein distance
- Wealth distribution equations
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty