Electronic Communications in Probability

Chaoticity of the stationary distribution of rank-based interacting diffusions

Julien Reygner

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Abstract

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.

Article information

Source
Electron. Commun. Probab., Volume 20 (2015), paper no. 60, 20 pp.

Dates
Accepted: 27 August 2015
First available in Project Euclid: 7 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465320987

Digital Object Identifier
doi:10.1214/ECP.v20-4063

Mathematical Reviews number (MathSciNet)
MR3399811

Zentralblatt MATH identifier
1333.60209

Subjects
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]
Secondary: 60F05: Central limit and other weak theorems

Keywords
Rank-based interacting diffusions nonlinear diffusion process stationary distribution chaoticity Wasserstein distance

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

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


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