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.(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Correlation Function of the Ornstein-Uhlenbeck Process

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