Actually starting at Arkin Lab
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.