A Rigorous Definition of Data Generating Process (DGP) I am trying to find a rigorous mathematical definition of a data generating process (DGP) under a well-defined probability space.
The closest source I have found on Cross Validated is this one, and it seems to come from a Evans and Rosenthal textbook (see the post).
Are there other rigorous definitions of a DGP or a reference textbook that has the definition you can share?

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*Added Remark: Maybe just the definition of a data generating process is a joint probability distribution of a set of stochastic processes?


The DGP may not have a rigorous definition. It is just whatever happens in the real world that gives rise to the data. We can attempt to model it, but we should not "confuse the map for the territory".
