It is often said that a AR(1) process can be viewed as a discretized version of the continuous-time Ornstein-Uhlenbeck process. Can we really claim this to be valid considering that the Ornstein-Uhlenbeck process is mean-reverting while AR(1) does not have to be. It seems to me that a discretized Ornstein-Uhlenbeck process is a subset of AR(1).
How could we expand this to VAR processes and find their continuous-time counterparts?
We could claim by the same analogy that a VAR process can be viewed as a discretized multi-dimensional Ornstein-Uhlenbeck process, although we're still ending up with a mean-reverting process - more of a special case?
