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Large rank-based models with common noise

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  • Kolli, Praveen
  • Sarantsev, Andrey

Abstract

For large systems of Brownian particles interacting through their ranks introduced in (Banner et al., 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 et al., 2013).

Suggested Citation

  • Kolli, Praveen & Sarantsev, Andrey, 2019. "Large rank-based models with common noise," Statistics & Probability Letters, Elsevier, vol. 151(C), pages 29-35.
    • Handle: RePEc:eee:stapro:v:151:y:2019:i:c:p:29-35
    DOI: 10.1016/j.spl.2019.03.005
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    References listed on IDEAS

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    1. Jianqing Fan & Yuan Liao & Han Liu, 2016. "An overview of the estimation of large covariance and precision matrices," Econometrics Journal, Royal Economic Society, vol. 19(1), pages 1-32, February.
    2. Gess, Benjamin & Souganidis, Panagiotis E., 2017. "Stochastic non-isotropic degenerate parabolic–hyperbolic equations," Stochastic Processes and their Applications, Elsevier, vol. 127(9), pages 2961-3004.
    3. B. Jourdain, 2000. "Diffusion Processes Associated with Nonlinear Evolution Equations for Signed Measures," Methodology and Computing in Applied Probability, Springer, vol. 2(1), pages 69-91, April.
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