Basically, The Ornstein-Uhlenbeck (OU) process (and its time-integral) decribes the velocity of a brownian particle. The OU process is Stationary (in time), Stochastic AND Markovian. 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.