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I will try to complete DFD very soon in such a way you can use it for part 2
A DFD is a no-brainer but how many people initially explain things to others in this way before grunge code, for example?
I would like to this problem a bit of a whack in C++. Ideally, C++20 and possibly Boost C++ libraries.Re "can always be integrated out".
It's not clear to me what is being asserted.
It's true that, in Hidden Markov Models, for example, there is indeed a lot of integrating out. I have a whole chapter on "Stochastic Volatility as a Hidden Markov Model" in my "Option Valuation under Stochastic Volatility II" book.
Separately, Dupire/Gyongy theory does a lot of integrating out of univariate or multivariate stochastic volatility in the construction of a local volatility surface for diffusions.
However, there remains the problem of "re-calibration".
In any event, if you can make/prove a careful statement about the application of your theory to data generating processes with additional state variables (hidden or not), my suggestion is to include that in your paper.