I was asked to implement an Ornstein-Uhlenbeck process in one of my simulations. I have coded the process to visualize the results and I was wondering, if my first value is at the mean, why bother using an O-U process? I thought the advantage of an O-U process is that it is mean-reverting, but if I am starting at the mean and just want to fluctuate about the mean, would a random Normal generator work equally well? Do I gain anything with the O-U model?
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A random normal generator would not expose serial correlations (it looks like noise and is not path-dependent), whereas a OU process is path-dependent:
See here for an example of an OU process
( Unfortunately this web-app can't display a random normal generator. )
The choice between the two depends on the application.
answered Jun 6, 2013 at 17:31
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1$\begingroup$ this is the first time in over a year I've actually found a use for my web-app! $\endgroup$ Commented Jun 6, 2013 at 17:33
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$\begingroup$ My application involves varying quantities throughout a simulation that are not normally varied (but have a certain probability distribution) and seeing how the output varies. Based on what you have said, I don't believe I actually need an O-U process as I will be time-averaging over all the changes (eliminating any serial correlations). Does that sound correct to you? $\endgroup$– BlinkCommented Jun 6, 2013 at 17:50
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$\begingroup$ What quantities are you varying? $\endgroup$ Commented Jun 6, 2013 at 17:52
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$\begingroup$ The simulation is a multiphase mixture (sand + air). I am varying the coefficient of restitution of the sand throughout the simulation (every x seconds). Because I don't know the exact value of the coefficient, I am using a distribution (which I want to sample from). The results will be time averaged, which should eliminate all serial correlations. $\endgroup$– BlinkCommented Jun 6, 2013 at 18:01
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$\begingroup$ Time averaging won't eliminate all serial correlations. What exactly is the process measuring? If the process is just noise, then sure, use normal generations, but if the next value of the process depends on the previous (for example, how a cumulative sum at time $t$ depends on the cumulative sum at time $t-1$), I would use something else. $\endgroup$ Commented Jun 6, 2013 at 18:07