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Re:Gaussian Processes, not quite for dummies by CrazyStat on Tuesday September 17, 2019 @10:45AM (#20995728)
> This stochastic process is a Gaussian process if for each t in R X_t has Gaussian distribution.

This is not quite strong enough. You need (X_t1, X_t2, ..., X_tn) to jointly have a multivariate Gaussian distribution for every finite (t1, ..., tn).

Re:Gaussian Processes, not quite for dummies by graycat on Tuesday September 17, 2019 @03:29PM (#20999130)
Usually! I gave a weak definition!

Also, for correlation, need to assume the expectations exist.