User:Carl Boettiger/Notebook/Stochastic Population Dynamics/2010/06/02

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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 with M. Samoilov

 * Kurtz Theorems: two limits, timescale and system size, often taken in the wrong order in practice.
 * Einstein-Smoluchowski debate regarding Langevin correspondence to Ito vs Statonvich representations resolved: [theorem]. (Statonvich is the more natural interpretation of the way in which we measure data to compare to Langevin.  Of course Ito and Stratonvich can be mapped back and forth anyway).
 * Of course this difference doesn't exist, and nothing goes wrong / no stochastic surprises if dynamics are linear.
 * Necessary limits of applicability not often checked in SDE famework.
 * Deterministic limit often works better than these limits would imply, as the same deterministic equation arises from multiple cases
 * Hamiltonian-Jacobi derivation sheds some light on why deterministic result is more general (requires fewer assumptions/weaker limits than SDE approach)
 * Intrinsic + extrinsic noise is hard. Environmental noise poorly defined, hard to make physical.  Can be incorporated into the master equation directly in a more meaningful way, still very hard problem.  Still, environmental noise often not needed to capture the behavior once we go back to original master equation.
 * References and examples to come.


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