When does the mean and variance define an SDE?

· Christopher Rackauckas · Nov. 1, 2021, 6:21 p.m.
Summary
I recently saw a paper that made the following statement: "Innes et al. [22] trained neural SDEs by backpropagating through the operations of the solver, however their training objective simply matched the first two moments of the training data, implying that it could not consistently estimate diffusion functions." However, given that the statement "could not consistently estimate diffusion functions" had no reference to it and no proof in the appendix, I was interested to figure out the mathema...
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