The Ornstein–Uhlenbeck process is a process defined as
with . Physically, this equation can be motivated as follows: a particle of mass  with velocity  moving in a medium, e.g., a fluid, will experience a friction force which resists motion whose magnitude can be approximated as being proportional to particles velocity  with .  Other particles in the medium will randomly kick the particle as they collide with it and this effect can be approximated by a white noise term; . Newtons second law is written as
Taking  for simplicity and changing the notation as  leads to the familiar form .
The corresponding Fokker–Planck equation is
The stationary solution () is