Ornstein Uhlenbeck with drift

1. Is Ornstein Uhlenbeck a Markov process?
2. What type of process is described by the Ornstein Uhlenbeck model?

Is Ornstein Uhlenbeck a Markov process?

The Ornstein–Uhlenbeck process is a stationary Gauss–Markov process, which means that it is a Gaussian process, a Markov process, and is temporally homogeneous. In fact, it is the only nontrivial process that satisfies these three conditions, up to allowing linear transformations of the space and time variables.

What type of process is described by the Ornstein Uhlenbeck model?

The Ornstein-Uhlenbeck process is a diffusion process that was introduced as a model of the velocity of a particle undergoing Brownian motion. We know from Newtonian physics that the velocity of a (classical) particle in motion is given by the time derivative of its position.