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

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 * style="background-color: #EEE"|[[Image:owwnotebook_icon.png|128px]] Stochastic Population Dynamics
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 * style="background-color: #F2F2F2" align="center"|  |Main project page


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Meeting

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

$$ \frac{X_1 + ... + X_n}{\sqrt{\sigma^2 n}} \propto N(0,1) $$

where

$$ \sigma^2 = E X^2 + 2 \sum_{i,j}^n Cov(X_i, X_j) $$


 * 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.


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