Large Rank-Based Models with Common Noise

Praveen Kolli; Andrey Sarantsev

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arXiv · 1802.06282

Large Rank-Based Models with Common Noise

Praveen Kolli·Andrey Sarantsev

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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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Praveen Kolli, Andrey Sarantsev. 2018-02-17. Large Rank-Based Models with Common Noise. https://arxiv.org/abs/1802.06282

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