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Now, I've done an exact, one dimensional, numerical simulation of the OU process similar to D. T. Gillespie in his article: Phys. Rev. E 54, 2084 (Aug. 1996) titled:

*Exact numerical simulation of the Ornstein-Uhlenbeck process and its integral*

The thing is, I was reading the "Correlation Function"-article on Wikipedia which stated, and I quote:

"(...), the study of correlation functions is similar to the study of probability distributions. Many stochastic processes can be completely characterized by their correlation functions; the most notable example is the class of Gaussian processes."

**I wonder if the OU process is completely characterized by it's correlation functions, and if so, how do we derive them AND show this; assuming we have Empirical/Numerical data of the process?**

Any help, tips or constructive advice is most appriciated.