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?



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

This is a common misunderstanding in causal inference, it produce any sort of ambiguities and contradictions. In causal inference the DGP is not a synonym for joint distribution, it is a different thing. For some details read here: What's the DGP in causal inference?
