Large Rank-Based Models with Common Noise
Probability
2019-05-13 v6
Abstract
For large systems of Brownian particles interacting through their ranks introduced in (Banner, Fernholz, Karatzas, 2005), the empirical cumulative distribution function satisfies a porous medium PDE. However, when we introduce a common noise, the limit is no longer deterministic. Instead, we show that this limit is a solution of a stochastic PDE related to this porous medium PDE. This stochastic PDE is somewhat similar to the equations developed for conservation laws with rough stochastic fluxes (Lions, Perthame, Souganidis, 2013).
Keywords
Cite
@article{arxiv.1802.06282,
title = {Large Rank-Based Models with Common Noise},
author = {Praveen Kolli and Andrey Sarantsev},
journal= {arXiv preprint arXiv:1802.06282},
year = {2019}
}
Comments
8 pages. Keywords: competing Brownian particles, porous medium equation, weak convergence, Wasserstein distance, empirical measure