• Corpus ID: 8242356

Self-organized criticality via stochastic partial differential equations

  title={Self-organized criticality via stochastic partial differential equations},
  author={Viorel Barbu and Philippe Blanchard and Giuseppe Da Prato and Michael Rockner},
  journal={arXiv: Probability},
Models of self-organized criticality, which can be described as singular diffusions with or without (multiplicative) Wiener forcing term (as e.g. the Bak/Tang/Wiesenfeld- and Zhang-models), are analyzed. Existence and uniqueness of nonnegative strong solutions are proved. Previously numerically predicted transition to the critical state in 1-D is confirmed by a rigorous proof that this indeed happens in finite time with high probability. 
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