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

From OpenWetWare
Jump to navigationJump to search
Owwnotebook icon.png Stochastic Population Dynamics Report.pngMain project page
Resultset previous.pngPrevious entry      Next entryResultset next.png

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.