Is a normal process mean reverting

Question

A normal process has a lot of outcomes around the mean and then fewer and fewer outcomes away from the mean. From this, can we conclude that a normal process reverts to the mean whenever it gets a certain distance away from the mean? In that sense, is a normal process the same as a mean reverting process?

Answer 1

If by a "normal process" you mean that $Y_t\sim N(\mu,\sigma^2)$ with the $Y$'s independent of each other then its mean - both unconditional and conditional on previous $Y$'s - is always $\mu$.

That's stronger than mean-reversion, since the conditional mean doesn't ever deviate from $\mu$, no matter how far from $\mu$ the previous observation was.

If you meant something else, you need to be more specific about your intent.