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mattja / sdeint

Numerical integration of Ito or Stratonovich SDEs
GNU General Public License v3.0
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Noise coefficient #11

Open ruiixu23 opened 7 years ago

ruiixu23 commented 7 years ago

I hope it's not a too stupid question since I have no background in SDEs in general but I need to use the package to generate sample paths for our machine learning project.

From my understanding, suppose I have a set of SDEs with d states, if I assume independent additive constant diffusion noise, then the G function should return a dxd diagonal matrix right? Should the entries of the matrix contain the "variance or std" of the noise? I am not even sure if the terms variance and std are proper here.

Thanks a lot for helping.

mattja commented 6 years ago

Yes, in that case the G function should return a constant dxd diagonal array.

Very roughly speaking, the entries correspond to std, not variance. More precisely, if function f were zero (no drift) then for a diagonal G the diffusion process would have its mean at the initial value and the variance in each direction increasing linearly with time, at a rate proportional to the square of those entries.