User:Carl Boettiger/Notebook/Stochastic Population Dynamics/2010/04/08

Stochastic Population Dynamics

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Research Reviewed timescales manuscript. Revisiting Stochastic Population Dynamics Main project page Previous entry      Next entry Meeting 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] where [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. Goals / To Do send Alan manuscript outline on ergodicity problem Finish both reviews variance of variance calculation!