Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 20 (2015), paper no. 60, 20 pp.
Chaoticity of the stationary distribution of rank-based interacting diffusions
We consider Brownian diffusions on the real line, interacting through rank-dependent drifts. It is known that in the mean-field limit, such particle systems behave like independent copies of a so-called nonlinear diffusion process. We prove a similar asymptotic behaviour at the level of stationary distributions. Our proof is based on explicit expressions for the Laplace transforms of the stationary distributions of both the particle system and the nonlinear diffusion process, and yields convergence of the marginal distributions in Wasserstein distances of all orders. We highlight the consequences of this result on the study of rank-based models of equity markets, such as the Atlas model.
Electron. Commun. Probab., Volume 20 (2015), paper no. 60, 20 pp.
Accepted: 27 August 2015
First available in Project Euclid: 7 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]
Secondary: 60F05: Central limit and other weak theorems
This work is licensed under a Creative Commons Attribution 3.0 License.
Reygner, Julien. Chaoticity of the stationary distribution of rank-based interacting diffusions. Electron. Commun. Probab. 20 (2015), paper no. 60, 20 pp. doi:10.1214/ECP.v20-4063. https://projecteuclid.org/euclid.ecp/1465320987