• Corpus ID: 233407593

Stochastic partial differential equations arising in self-organized criticality

  title={Stochastic partial differential equations arising in self-organized criticality},
  author={Lubom{\'i}r Ba{\~n}as and Benjamin Gess and Marius Neu{\ss}},
Scaling limits for the weakly driven Zhang and the Bak-Tang-Wiesenfeld (BTW) model for self-organized criticality are considered. It is shown that the weakly driven Zhang model converges to a stochastic PDE with singular-degenerate diffusion. In addition, the deterministic BTW model is proved to converge to a singular-degenerate PDE. Alternatively, the proof of convergence can be understood as a proof of convergence of a finite-difference discretization for singular-degenerate stochastic PDE… 
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