Chaoticity of the stationary distribution of rank-based interacting diffusions

2014/08/18 by Julien Reygner, Reygner, Julien
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications

paper · doi:10.48550/arxiv.1408.4103

openalex publication_date 2014/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The mean-field limit of systems of rank-based interacting diffusions is known to be described by a nonlinear diffusion process. We obtain a similar description at the level of stationary distributions. Our proof is based on explicit expressions for the Laplace transforms of these stationary distributions 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.

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