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

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Meeting

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

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \frac{X_1 + ... + X_n}{\sqrt{\sigma^2 n}} \propto N(0,1) }

where

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \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.