User:Carl Boettiger/Notebook/Stochastic Population Dynamics/2010/03/05

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  • Basically I want to apply central limit theorem for stationary processes (accounts for covariances), assuming mean zero

[math]\displaystyle{ \frac{X_1 + ... + X_n}{\sqrt{\sigma^2 n}} \propto N(0,1) }[/math]


[math]\displaystyle{ \sigma^2 = E X^2 + 2 \sum_{i,j}^n Cov(X_i, X_j) }[/math]

  • Discussion of Freidlin–Wentzell theory in connection to Arrhenius law and the well-defined stochastic tipping point which occurs before the branch point.
  • Kurtz results don't really help in the case of ergodicity, can make statements about the (even non-stationary) ensemble limit.