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.
- Pub Date:
- November 2008
- Mathematics - Probability;
- Mathematical Physics;
- Mathematics - Analysis of PDEs
- Theta Series in Advanced Mathematics, "Potential Theory and Stochastic Analysis" in Albac. Aurel Cornea Memorial Volume, 2009, pp. 11-19