Large Rank-Based Models with Common Noise

2018/02/17 by Kolli, Praveen, Sarantsev, Andrey · 1 citation
#60H10 #60H15 #60J55 #60K35 #91B28 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1802.06282

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).

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