Propagation of chaos for rank-based interacting diffusions and long time behaviour of a scalar quasilinear parabolic equation

@article{Jourdain2013PropagationOC,
  title={Propagation of chaos for rank-based interacting diffusions and long time behaviour of a scalar quasilinear parabolic equation},
  author={Benjamin Jourdain and Julien Reygner},
  journal={Stochastic Partial Differential Equations: Analysis and Computations},
  year={2013},
  volume={1},
  pages={455-506}
}
We study a quasilinear parabolic Cauchy problem with a cumulative distribution function on the real line as an initial condition. We call ‘probabilistic solution’ a weak solution which remains a cumulative distribution function at all times. We prove the uniqueness of such a solution and we deduce the existence from a propagation of chaos result on a system of scalar diffusion processes, the interactions of which only depend on their ranking. We then investigate the long time behaviour of the… CONTINUE READING

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